GENEVA - The United Nations mediator for Syria, Lakhdar Brahimi, wrapped up the second round of peace talks Saturday without breaking a long-standing deadlock or setting a date for a third round and urged the parties to think seriously about their commitment to the negotiations.

Brahimi said the talks had broken down primarily because the Syrian government balked at his suggestion that the negotiators discuss both sides’ top demands early on, rather than spending days on the government’s demands.

“I am very, very sorry, and I apologize to the Syrian people,” Brahimi, an Algerian diplomat who has spent decades negotiating thorny conflicts, said after a 45-minute meeting with the two sides ended in disagreement. “I apologize to them that on these two rounds we haven’t helped them very much.”

The dispiriting finish called into question the future of the talks. In two rounds, the talks have produced no negotiations on resolving a conflict that has killed more than 135,000 people and driven 9.5 million from their homes, even though they are sponsored by Russia and the United States and backed by dozens of other countries.

“It’s not good for Syria that we come back for another round and fall in the same trap that we have been struggling with this week and most of the first round,” Brahimi said. “So I think it is better that every side goes back and reflect and take their responsibility: Do they want this process to take place or not? I will do the same.”

He said he would report to the U.N. secretary-general, Ban Ki-moon, and push for a meeting with Ban; U.S. Secretary of State John Kerry; and the Russian foreign minister, Sergei Lavrov. Some Western diplomats have suggested that Brahimi, 80, might be worried about harming his legacy by presiding over empty talks and that he might recommend ending them.

Western officials were quick to call for new pressure on the Syrian government. Minutes after Brahimi spoke, the British foreign secretary, William Hague, tweeted that the U.N. Security Council “must now act to address the humanitarian crisis urgently.” But Russia, the Syrian government’s most powerful backer, sees Western attempts to require access for aid workers as a pretext for military action, and it has blocked previous Security Council measures on Syria.

Brahimi said at a news conference that both sides agreed that the agenda for the next round should focus on four points: ending the violence and terrorism, creating a transitional governing body, building national institutions, and reconciliation.

“Unfortunately the government has refused, which raises the suspicion of the opposition that in fact the government doesn’t want to discuss the [transitional governing body] at all,” Brahimi said.

Bashar al-Jaafari, the Syrian ambassador to the United Nations in New York and the government’s lead negotiator, said it was impossible to resolve the issue of terrorism in one day, and that the government wanted to reach “a common vision” on the subject before moving on to others.

But Brahimi said he had made it “very clear” that both topics would take far more than one day, and that his aim was simply to ensure that the two sides at least began to discuss each other’s demands.

Each side blamed its opponents and their international backers for the lack of progress.

“We are here to negotiate,” said Louay Safi, an opposition spokesman. “We have been disappointed completely, not only by the regime.”

Russian officials “have not prevailed over the regime that wants to stall,” Safi said, adding that Russia “continues to supply” the weapons that the government is using to bombard rebel-held towns and neighborhoods.

Al-Jaafari, the government negotiator, said the government recognized that the opposition delegation could not single-handedly stop terrorism in Syria because it does not control many of the insurgent groups. But, he added, officials want to hear that the opposition is committed to stopping it.

“We promised our own people to get back to Geneva to continue the Geneva talks as long as it takes, because we are extremely careful about stopping the bloodshed in Syria and combating terrorism,” Jaafari said. “This I promise you: We will be committed to doing so.”

The opposition has condemned violence against civilians and pointed to recent battles between its affiliated fighters and jihadist groups. But the crux of the dispute is the definition of terrorism, which the government says includes all armed opposition.

Two senior opposition figures said Saturday that the government has put the top members of the Syrian National Coalition, the main opposition group in exile, on a terrorist list and ordered confiscation of their assets. They said the list includes the coalition’s president and vice presidents as well as others including members of the political committee.

Meanwhile, Syrian troops pressed an offensive near Lebanon on Saturday, heavily bombarding a rebel-held town and forcing many residents to flee to safety across the border, activists said.

The violence came as an activist group said the death toll in the three-year Syrian conflict has reached 140,000. The Britain-based Syrian Observatory for Human Rights said the figure includes civilians, rebels, members of the military, pro-government militiamen and foreign fighters.

The group based its count on information from a network of informants inside the country.

Information for this article was contributed by Anne Barnard and Nick Cumming-Bruce of The New York Times and by John Heilprin and Bassam Mroue of The Associated Press.

Front Section, Pages 6 on 02/16/2014