More than a thousand Syrians have fled to Lebanon after weeks of attacks on the town of Homs and other areas.
The Associated Press said that as many as 2,000 people had crossed the border with only the possessions they could carry.
"We fled the shelling and the strikes," said Hassana Abu Firas, from Qaa in northeast Lebanon.
"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."
Also on Monday Kofi Annan, special envoy for the UN and the Arab League, confirmed that he will travel to Damascus on 10 March "to seek an urgent end to all violence and human rights violations, and to initiate the effort to promote a peaceful solution to the Syrian crisis".
The former UN secretary general will be joined by Nasser al-Qudwa, who is the former foreign minister of the Palestinian Authority and Yasser Arafat's nephew.
He will also be preceded by UN relief chief and former Labour cabinet minister Valerie Amos, who will visit the Syrian capital to "urge all parties to the conflict to allow unhindered access for aid workers to evacuate the wounded and deliver essential humanitarian supplies".
"The Syrian authorities have confirmed that I can visit Syria this week. I will arrive in Damascus on Wednesday 7 March and leave on Friday 9 March," Amos, Under-Secretary-General for Humanitarian Affairs, said in a statement.
Aid agencies were still unable to distribute vital medical supplies in the Baba Amr district of Homs, Syria, and the International Committee of the Red Cross (ICRC) said that the Syrian army was blocking access to the neighbourhood where hundreds died in four weeks of shelling by government troops.
Instead the ICRC gave out aid in neighbouring districts.
A spokesperson said in an emailed statement: "Teams started distributing food, blankets, hygiene kits in two districts of Al-Tawzii and Al-Insha'at in Homs city.
"These are areas close to Baba Amr which received a lot of displaced residents during the fighting. This is following our trip to the Abel village yesterday, where we distributed assistance to residents and population displaced from Baba Amr."
Supporters of President Bashar al-Assad held a rally near to the Russian embassy to show their support for re-elected Russian leader Vladimir Putin, whose government has refused calls to condemn the Syrian leader and vetoed UN resolutions calling for him to quit.
More recently, however, Putin indicated a shift in his position, saying that it was down to the Syrian people to choose their leader and calling on both sides to end the violence.
China, the other permanent UN security council member who also vetoed a resolution decrying the violence, has outlined its own six-point plan to defuse the situation.
Their plan includes calls to "immediately, fully and unconditionally cease all acts of violence" and "respect the independence" of the country's people in choosing their leader.