BEIRUT - The Syrian opposition called on Hezbollah to withdraw its fighters from the country, as activists said regime troops supported by gunmen linked to the Lebanese Shiite militant group battled rebels Sunday for control of a string of villages near the Lebanon-Syria border.

Outside the capital, Damascus, activists said they had documented the names of 80 people killed in a government assault on the area over the past five days.

The Syrian National Coalition - the main Western-backed opposition group - warned that Hezbollah involvement in Syria’s civil war could lead to greater risks in the area, and urged the Lebanese government to “adopt the necessary measures to stop the aggression of Hezbollah” and to control the border to “protect civilians in the area.”

The statement, posted on the Coalition’s Facebook page,coincided with a surge in fighting around the contested town of Qusair in Syria’s Homs province near the frontier with Lebanon.

Over the past two weeks, the Syrian military, supported by a Hezbollah-backed militia, has pushed to regain control of the border area. The region is strategic because it links Damascus with the Mediterranean coastal enclave that is the heartland of President Bashar Assad’s Alawite sect, an offshoot of Shiite Islam.

The fighting also points to the sectarian nature of the Syrian conflict, which pits a government dominated by the president’s Alawite minority against a primarily Sunni Muslim rebellion, and underscores widely held fears that the civil war could drag in neighboring states.

The pro-regime gunmen are members of the Popular Committees, which were set up last year in Syria with Hezbollah’s backing to protect Syrian villages inhabited by Lebanese Shiites, although rebels accuse the fighters of attacking opposition villages in the area and fighting alongside government forces.

While Hezbollah confirms backing the Popular Committees, it denies taking part in Syria’s civil war.

The fighting along the border region has flared in recent weeks, and on Saturday government forces captured the villages of Radwaniyeh and Tel al-Nabi Mando. On Sunday, regime forces shelled the villages of Abu Houri, Saqarigh, Nahriyeh and Ein al-Tanour in the Qusair region, according to the Britain-based Syrian Observatory for Human Rights activist group. It said at least four rebels were killed in the fighting.

Syrian state television said the army was trying to “uproot all the terrorists from the area.” The government, which denies it is facing a popular uprising, describes the revolt as a foreign-backed plot and calls those trying to topple it “terrorists.”

Lebanon’s state-run news agency reported two shells fired from Syria landed Sunday in the border town of Hermel, causing material damage but no casualties. A day earlier, two mortar rounds landed in the town for the first time, marking an escalation in violence along the already tense frontier.

Inside Syria, the Observatory said it had documented the names of 80 people, including three children and six women, who were killed in the past five days in the areas of Jdaidet Artouz and Jdaidet al-Fadel west of Damascus.

One amateur video posted online showed seven bodies, some shot in the face, placed in black body bags on the ground. The videos appeared genuine and corresponded to other Associated Press reporting of the events depicted.

The U.S. has long called for Assad to leave power, but for months did not play an active role in backing the rebellion. Recently, however, Washington has grown more assertive, helping cobble together the Syrian National Coalition late last year in the hopes that it could unite the deeply divided opposition and provide a conduit for aid to rebels on the ground.

At a conference on Saturday in Istanbul that brought together the opposition leadership and its chief international supporters, U.S. Secretary of State John Kerry announced that President Barack Obama’s administration would double its nonlethal assistance to the Syrian opposition with an additional $123 million in supplies. That could include for the first time armored vehicles, body armor, night vision goggles and other defensive military supplies, officials said.

The additional aid brings total nonlethal U.S. assistance to the opposition to $250 million since the fighting began more than two years ago. Washington has refused so far to provide weapons to Syria’s rebels out of fears they could fall in the hands of extremists.

The U.S. pledge was the only tangible public offer of new international support at the meeting of the foreign ministers of the 11 main countries supporting the opposition and fell well short of what the opposition has been appealing for: weapons and direct military intervention to stop the violence that has killed more than 70,000 people.

“I can’t tell you how quickly it will change things on the ground,” Kerry said Sunday. “I can promise you that as soon as I return to Washington, I am going to press as hard as I can” to get it to the opposition within a matter of weeks. “This has to happen quickly, it has to have an impact,” he said.

The Syrian National Coalition is seeking drone strikes on sites from which the regime has fired missiles, the imposition of no-fly zones and protected humanitarian corridors to ensure the safety of civilians.

On Sunday, Coalition president Mouaz al-Khatib submitted his resignation, according to a statement on the organization’s Facebook page. The Coalition said it would take up the matter at its next meeting, without providing a date.

Al-Khatib, a respected Muslim preacher seen as a uniting figure and moderate, tried to quit his post in March, citing frustration over what he called a lack of international support and constraints imposed on the body itself. The Coalition rejected his resignation then, and he agreed to stay on until his six-month terms ends in May.

Information for this article was contributed by Maamoun Youssef and Matthew Lee of The Associated Press.

Front Section, Pages 6 on 04/22/2013