KYIV, Ukraine -- President Vladimir Putin insisted Sunday that he was willing to negotiate over his invasion of Ukraine, an oft-repeated line that U.S. and Ukrainian officials have dismissed as lip service, as air-raid sirens sent Ukrainians already on edge from months of war and bitter cold to seek shelter on Christmas Day.
One nationwide alert in the morning and a second in the afternoon were lifted within about two hours, and there were no immediate reports of Russian strikes landing in Ukraine. But the air-raid warnings added to the anxiety of the country's first Christmas since Russia's invasion, after days of warnings from officials that Putin's forces would unleash a new wave of strikes targeting energy infrastructure.
As Ukrainians marked the holiday with resilience, gathering despite the sirens in churches and chapels for Christmas services, Putin repeated the claim that his war was in defense of Russia's national interests and that Ukraine and its allies were to blame for a conflict that has entered its 11th month.
He said in a state television interview, excerpts of which were released Sunday afternoon, that Russia is "prepared to negotiate some acceptable outcomes with all the participants of this process."
He said "it's not us who refuse talks, it's them" -- something the Kremlin has repeatedly stated in recent months as its 10-month old invasion kept losing momentum.
Putin also repeated that Moscow has "no other choice" and said he believed the Kremlin was "acting in the right direction."
"We're defending our national interests, the interests of our citizens, our people," he said.
Putin's remarks come as attacks on Ukraine continue. A countrywide air raid alert was announced twice Sunday, and three missiles in the afternoon hit the city of Kramatorsk in the partially occupied Donetsk region, local officials reported.
The missiles hit an industrial area of the city, and there weren't any casualties, according to the Ukrainian governor of Donetsk, Pavlo Kyrylenko. Kyrylenko said the city of Avdiivka was also attacked Sunday with six rounds of shelling, and a woman was wounded there.
Top Russian officials have frequently said they are prepared to enter negotiations -- Putin said last week that his goal was "to end this war" -- while emphasizing almost in the same breath a determination to keep fighting. U.S. officials have said Russia has offered no indications that it is prepared to negotiate in good faith.
On Sunday, Ukrainians appeared determined to celebrate as ordinary a holiday as possible.
"Nobody canceled birthdays, and nobody canceled Christmas," said Oleh Moor, 50, a cook in Kyiv. "You cannot tell a child, 'Wait until the war is over.' Maybe there is no music, maybe there are no concerts like last year, but we continue living."
Because of Russian strikes on infrastructure, the Ukrainian capital is mostly devoid of holiday lights and decorations, but authorities did set up a generator-powered Christmas tree on a central square that has continued to shine even during the frequent blackouts.
On Sunday, Moor and his family were passing it on their way to Christmas dinner. His children posed for photographs with Santa Claus.
"We won't let the enemy know we are broken," Moor said.
There have been no serious peace talks between Russia and Ukraine in months, and Ukrainian officials have said they will not negotiate until Moscow withdraws its troops. On Sunday, Ukrainian officials were quick to dismiss Putin's remarks, with Mykhailo Podolyak, a senior presidential adviser, saying the Russian leader "needs to come back to reality."
"Russia doesn't want negotiations but tries to avoid responsibility," Podolyak wrote on Twitter.
Through the fall and start of winter, Russian forces have fired volleys of cruise missiles and launched drones at Ukrainian cities, aimed at energy and heating infrastructure. Military analysts have said it is part of a Russian strategy of plunging the country into darkness and cold to demoralize the population.
The bombardments have typically come at intervals of about a week. The actions Sunday that touched off the air alert could have been either Russia firing missiles or sending planes that set off false alarms.
But the air-raid alarms are disruptive even when sounded as a precaution and no actual strikes follow.
During the alerts, Ukrainians often move to corridors, bathrooms or other areas in their homes that are away from windows and deemed safer in case of a strike. Some people go to basements or quickly bundle their children into warm clothing to seek shelter in a subway station.
Ukrainians in the capital have also pinned their hopes on the country's air defenses.
But in towns closer to the front line, no defenses can shield against artillery fire. On Sunday, Ukraine's defense minister, Oleksii Reznikov, said in a post on Twitter that artillery had destroyed the only church in the village of Kyselivka, in the Kherson region in southern Ukraine.
One ripple effect of the war has been a shift in views of when Christmas should be celebrated, with more Orthodox Ukrainians now saying they want to do so Dec. 25, in line with most of Europe, rather than on the Eastern Orthodox liturgical calendar date of Jan. 7. Over the past year, support for celebrating Christmas in December has risen sharply. A social survey by Rating Group, a polling agency, showed that 44% of Ukrainians want to celebrate in December, up from 26% of those polled last year.
On Sunday, churchgoers crowded the small chapel of the St. Sophia Cathedral in Kyiv, one of the capital's oldest churches, for a Christmas service. Bundled up from the cold, they continued their prayers, unmoved, even as the morning's air-raid alarm sounded.
In Rome, Pope Francis appealed for peace in Ukraine during his Christmas address from the balcony of St. Peter's Basilica, asking God to "enlighten the minds of those who have the power to silence the thunder of weapons and put an immediate end to this senseless war."
The pope's plea came a day after Russian shelling ripped through the center of the southern city of Kherson, killing at least 10 people and prompting President Volodymyr Zelenskyy of Ukraine to say that the holidays "have a bitter aftertaste for us this year."
"Dinner at the family table cannot be so tasty and warm. There may be empty chairs around it," he said in a Christmas Eve message. "And our houses and streets can't be so bright. And Christmas bells can ring not so loudly and inspiringly. Through air-raid sirens or even worse -- gunshots and explosions."
Those sentiments were evident in Kyiv, where friends and relatives of Ukrainian prisoners of war gathered on Christmas Eve and staged a performance called "Christmas in Captivity," re-creating the image of the Last Supper that included barbed wire and empty steel bowls.
"We have this opportunity to gather at the abundant Ukrainian table, thanks to our soldiers who sacrifice their normal lives to protect us," said Yevhen Sukharnikov, one of the organizers, whose 24-year-old son is a prisoner of war.
"They are being moved all the time, and we are not provided with any way to contact them," Sukharnikov said.
Elsewhere in the front-line region, around the city of Bakhmut, where fierce battles have been underway in recent weeks, the Russian forces were struggling to keep up the pace of their offensive, a U.S.-based think tank reported this weekend.
"Russian forces' rate of advance in the Bakhmut area has likely slowed in recent days, although it is too early to assess whether the Russian offensive to capture Bakhmut has culminated," the Institute for the Study of War wrote in its recent update.
The think tank cited Russian military bloggers, who it said have recently acknowledged "that Ukrainian forces in the Bakhmut area have managed to slightly slow down the pace of the Russian advance around Bakhmut and its surrounding settlements."
Sources on Ukrainian social media "previously claimed that Ukrainian forces completely pushed Russian forces out of the eastern outskirts of Bakhmut" around Dec. 21, the report added.
"Russian forces will likely struggle to maintain the pace of their offensive operations in the Bakhmut area and may seek to initiate a tactical or operational pause," the institute concluded.
The toll from months of war continued to climb. The Ukrainian military said Sunday that three de-mining experts had been killed in the Kherson region a day earlier while clearing mines and unexploded ordnance left by the Russian military, which retreated from there last month.
The Russian forces shelled Ukrainian-held areas of the partially occupied Kherson region 71 times over the past 24 hours, including 41 attacks on the city of Kherson, the region's Ukrainian governor Yaroslav Yanushevich reported Sunday.
A total of 16 people have been killed, according to the official, including three emergency workers killed in the process of de-mining the Berislav district of the region. Yanushevich said 64 more have been wounded.
In the neighboring Dnipropetrovsk region, the city of Nikopol was shelled overnight from heavy artillery, Gov. Valentyn Reznichenko said. No casualties have been reported.
A day after the deadly attack in the city of Kherson, a long line formed Sunday at a blood donation center, photos shared by Ukrainian officials on social media showed. More than 60 people were wounded in the strikes, which hit a shopping area and residential buildings in one of the deadliest Russian attacks on the city in the nearly two months since it was reclaimed by Ukrainian forces.
"People have gathered to help their fellow city residents injured by yesterday's Russian terrorist attack," Ukraine's military tweeted. "Anger. Invincibility. Compassion. Victory."
Information for this article was contributed by Andrew E. Kramer and Anton Troianovski of The New York Times and by staff writers of The Associated Press.