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.