Syrian youth Ahmed, 13, (L) and Faris (R), 16, who allegedly fight alongside opposition fighters from the Sadeq Al-Amin Brigade, get prepared with another member of the brigade before a patrol in the Salah al-Din neighborhood of the northern Syrian city of Aleppo on Nov. 17, 2013. (Karam Al-Masri/AFP/Getty Images)

A new Syrian offensive in the mountainous terrain bordering Lebanon has triggered a fresh exodus of thousands of Syrians into a country already burdened by the largest number of refugees in the region, U.N. officials said Sunday.

A thousand families sought shelter between Friday and Sunday in the eastern Lebanese town of Arsal after government forces attacked their villages in Syria, according to the Office of the U.N. High Commissioner for Refugees.

The attack came as part of an escalating push by the Syrian government to cut rebel supply routes linking the suburbs of Damascus to Lebanon through the rugged Qalamoun mountains. The routes are one of the last lifelines between rebel positions in central Syria and the outside world after others through the city of Homs were shut down this summer.

Forces loyal to Syrian President Bashar al-Assad have been gaining momentum on a number of fronts as they seek to reclaim rebel-held territory ahead of peace talks due to be held in the coming months in Geneva.

The official Syrian Arab News Agency said government forces also made fresh advances on Sunday on the outskirts of Aleppo, where they have reversed more than a year of steady rebel gains in recent weeks.

Controlling the vast Qalamoun area will be a tough challenge because of the mountainous terrain and the onset of winter. But if rebel forces suffer setbacks in the strategic area, it would deal a blow to their efforts to sustain fighting in opposition strongholds around Damascus, where the government also has been making gains.

The latest fighting focuses on the small town of Qara, on the main highway linking Damascus to Homs, which has been closed by the fighting since Friday. Rebel commanders say government troops in the area are reinforced by fighters from the Shiite Lebanese Hezbollah movement, which controls much of the territory bordering Syria in eastern Lebanon.

The Britain-based Syrian Observatory for Human Rights said artillery and warplanes pounded Qara for a second day on Sunday, and video posted on YouTube showed smoke rising after one of the attacks.

Some Lebanese news organizations said tens of thousands of Syrians had arrived in Lebanon over the weekend, but U.N. officials who visited the border area counted 1,000 families, or about 4,000 to 5,000 people, the officials said.

The cold is the biggest problem for the new refugees, most of whom fled Qara under fire with few possessions, said Dana Sleiman, a spokeswoman for the UNHCR in Lebanon. They are taking refuge in mosques, homes, schools and a small tented camp, but “shelter is a problem,” she said after visiting the new arrivals.

“It’s extremely cold, and we have colder months coming ahead,” Sleiman said.

Arsal, a remote town of 80,000 that has become a haven for rebels and their families, has 30,000 refugees and lacks the capacity to care for many more, she said.

Lebanon, a country the size of Delaware, has been stretched to the limit by an influx of more than 816,000 refugees, who make up one-fifth of the population of the country. They are among more than 2.2 million Syrians who have fled the war raging in their country. Jordan and Turkey also are hosting large numbers of refugees.

More are expected as the battle for Qalamoun heats up, according to Sleiman.

“People will continue to come as long as they have no choice,” she said. “These people had no choice but to flee to Lebanon, and the first thing they told me was that they want to go home.”

Meanwhile, an explosion late Sunday targeting an administrative office in the northeastern Damascus suburb of Harasta killed at least 31 government troops, the Syrian Observatory for Human Rights said in a statement. There was no confirmation from the government.