Some 60,000 Syrians have fled since Wednesday from three towns to escape fighting between the Al-Qaeda-affiliated Al-Nusra Front and the Islamic State of Iraq and the Levant (ISIL), said the Syrian Observatory for Human Rights.
Meanwhile, talks on the rebel withdrawal from Homs -- once dubbed the "capital of the revolution" -- entered their final phase, a day after a ceasefire began in the strategic central city, which has seen some of the heaviest fighting of Syria's civil war.
A rebel pull-out would hand Assad complete control of the city and deal a major symbolic blow to the uprising, which began in March 2011 with mass rallies calling for democratic change but escalated into an insurgency when the regime launched a brutal crackdown.
"Talks to rid the city of arms and of armed men... are ongoing and we are near the end," said provincial governor Talal al-Barazi.
Abul Harith al-Khalidi, the rebel tasked with negotiating the deal, said the talks are being held in tandem with negotiations to free a group of pro-regime Iranian officers held by rebels in the northern city of Aleppo.
"We want to stop this bloodbath," he said.
Only a handful of neighbourhoods surrounding the now destroyed Old City remain in rebel hands, after a series of massive army offensives starting in February 2012.
The vast majority of some 1,500 people still trapped in the Old City are fighters, but the rebel-held Waer neighbourhood is home to hundreds of thousands of civilians,many of them displaced from fallen rebel bastions.
Barazi said the deal "will be applied first in the Old City, then in Waer. The goal is to reach a peaceful solution that brings back security and government institutions."
The impending defeat in Homs came as fighting flared between the two jihadist groups in the eastern Deir Ezzor province, following months of battles pitting Islamist and moderate rebels against ISIL, which is accused of kidnapping, torturing and killing opponents.
The Observatory, a Britain-based group relying on sources across Syria, said three towns -- Busayra, Abriha and Al-Zir -- had been virtually emptied of their inhabitants, and that both groups had torched several homes.
It said at least 62 militants had been killed in four days of fighting.
Elsewhere in Syria, the army advanced around Aleppo and took control of the road leading to the airport, according to a security source.
Aleppo's rebel areas have been under a massive aerial offensive since mid-December that has killed hundreds of people -- mainly civilians -- and forced thousands to flee.
Rebel mortar attacks Saturday on Aleppo struck a hospital, killing 12 people, and Aleppo University, wounding 22 civilians, mainly students, according to the SANA state news agency.
Mortar rounds also hit Damascus, killing three people, SANA said.
Three soldiers were killed in a car bombing in southwestern Damascus, the Observatory said.
But the army, backed by Lebanese Shiite Hezbollah fighters, made gains east of the capital, advancing into the rebel-held town of Mleiha after several weeks of daily bombardment, it said.
More than 150,000 people have been killed since Syria's uprising began and nearly half the population have fled their homes.
Assad meanwhile called for "greater cooperation" between his government and aid agencies at a meeting with officials, footage of which was broadcast by state television.
"There is a need for greater cooperation between ministries and the bodies involved in humanitarian aid, and to deliver aid without delay, and to work on the ground with all the local and international stakeholders to make aid delivery smoother," he said.
His remarks came after UN chief Ban Ki-moon issued a report saying that foreign aid was still not reaching millions of needy Syrians despite a Security Council resolution in February calling for greater access, singling out the government for particular censure.
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