Syrain refugees fleeing violence in their country have been pouring across the border into Lebanon, according to the United Nations.

The U.N. refugee agency said Monday as many as 2000 Syrians had crossed into Lebanon in the last two days, many arriving with bags filled with what few possessions they could carry.

We fled the shelling and the strikes, Hassana Abu Firas told the Associated Press.

Speaking from Qaa in northeast Lebanon, Hassana said she had fled with two other families from government shelling of their town al-Qusair, 14 miles across the border in Syria.

What are we supposed to do? People are sitting in their homes and they are hitting us with tanks. Those who can flee do. Those who can't will die sitting down, she said.

Al-Qusair is in Homs province, which over the past month has become a key battleground between fighters opposed to the rule of President Bashar al-Assad and government forces.

Opposition forces claim hundreds have been killed in the month-long Homs offensive, with the U.N. putting the overall death toll for the year-long rebellion at 7,500.

On Monday aid workers from both the Red Crescent and the Red Cross entered parts of the battered city for the first time after trying for days to get permission from government forces.

But Damsacus officials are still barring aid workers from entering the Baba Amr district of Homs, where heavy fighting has trapped residents for weeks.

Rebel fighters from the opposition Free Syrian Army were forced to abandon Baba Amr late last week as a result of the bombardment. Syrian forces have taken control of the area, and have blocked Red Cross trucks from entering, reportedly with land mines and booby traps.

According to the AP some 4,000 people are still living in the devastated neighborhood, suffering from cold, hunger and lack of medical supplies.

Activists claimed Syrian forces have kept aid workers out of Baba Amr as they have been hunting down and killing rebel fighters in the area.

Homs activist Mulham al-Jundi told the AP he had heard a few explosions in the neighborhood and saw columns of smoke there from a rooftop elsewhere in the city.

We have heard explosions in Baba Amr, so it seems that they are destroying some of the houses and important centers there, he said via Skype.