Thousands of Syrians fleeing a military brutal crackdown by the government of Bashar al-Assad have crossed into neighboring Lebanon, the United Nations says.

The reports came as the Syrian president told state media that his government was determined to press on with a planned reform program and to fight the "terrorists" it blames for the violence.

"The Syrian people, who have in the past managed to crush foreign plots ... have again proven their capacity to defend the nation and to build a new Syria through their determination to pursue reforms along with the fight against foreign-backed terrorism," SANA state news agency quoted Assad as saying on Tuesday.

Assad has been facing increasing anger over his government's apparent refusal to allow medical aid into a devastated, largely anti-government district in Homs, in addition to alleged rights abuses.

Dozens of men, women and children returned on foot to Baba Amr, passing buildings riddled with bullet holes and other damage.

The return comes days after revolution fighters pulled out of the neighborhood following a sustained heavy military assault.

'Smell of death'

The International Committee of the Red Cross (ICRC) says it is still awaiting approval to distribute aid in Baba Amr, which has been under siege by government forces for a month.

Residents who fled the district spoke of bodies decomposing under rubble, sewage mixing with litter in the streets, and a campaign of arrests and executions.

"The smell of death was everywhere. We could smell the bodies buried under the rubble all the time," Ahmad, who escaped to Lebanon, said.

"We saw so much death that at the end the sight of a dismembered body ... stopped moving us."

Fresh violence was reported by activists in the provinces of Homs, Deraa, Idlib, and Deir ez-Zor on Tuesday.

The Local Coordination Committees, an umbrella organization of opposition activists, claimed that at least 21 people were killed in that violence.

Rami Abdel Rahman, head of the UK-based opposition Syrian Observatory for Human Rights (SOHR), said government forces bombed a bridge used to evacuate the wounded and refugees to Lebanon from Homs.

The SOHR also reported that at least 12 people - including five government troops - had been killed in clashes in the town of Herak, in Deraa, after a major government assault on the town.

Al Jazeera is unable to independently verify the activists' claims because of restrictions on reporting imposed by the government.

Influx into Lebanon

As the Syrian government's crackdown continues, the UN's refugee agency says that about 2,000 refugees have crossed into Lebanon over the last two days.

In the hillside town of Arsal in Lebanon's Bekaa Valley, residents said between 100 and 150 families had arrived from across the border on Sunday in one of the biggest such refugee influxes so far.

A dozen families spent Sunday night in a three-storey apartment block in Arsal after fleeing what they said was a sustained army attack on the Syrian town of Qusair with tanks, rocket-propelled grenades and helicopters.

Refugees said that the Syrian army had arrested many others trying to flee, while some said Lebanese forces had prevented others from crossing the border.

Hassana Abu Firas, a refugee from Qusair, said: "We call on the Lebanese government and the Lebanese army to help us, to hide us, to hide our families, we don't want anything we just want the Lebanese government to help the Syrian people, we appeal to them, we call on them to help us, we call on the Muslims and the Arab governments to help us."

Diplomatic developments

International condemnation of Syria has increased in recent days, with John McCain, the influential US politician, calling on Barack Obama to launch air raids against Syria's military.

Speaking in the US senate on Monday, McCain said the administration had been too soft on Syria and cited moral and strategic obligations to help force Assad's government out of power.

The plea for greater US military involvement came a day before Li Huaxin, a Chinese diplomat, was due to arrive in Damascus to meet the Syrian foreign minister and to outline China's six-point plan for halting the violence.

Kofi Annan, the UN and Arab League's envoy, and Valerie Amos, the UN's humanitarian affairs chief, are also due to visit Damascus this week.

The UN says more than 7,500 civilians have died in the Syrian crackdown so far.

Syrian authorities said in December that 2,000 police and soldiers had been killed since protests, inspired by Arab uprisings which have overthrown four veteran leaders, erupted last March.

Lebanese security officials say more than 10,000 Syrians have crossed the border in search of refuge since March 2011. There are another 11,000 refugees in neighboring Turkey.

PHOTO CAPTION

Syrians walk past a Free Syrian Army fighter in the old city of Idlib, north Syria, Monday, March 5, 2012.

Al-Jazeera