Syrian army forces made advances on Friday around the Old City of Homs, where some 1,200 rebels are dug in and under regime siege, a security source told AFP.
In a government-held district of the city, meanwhile, 14 people were killed when a car bomb exploded outside a mosque after the weekly Muslim prayers, state television reported.
The army, which began a broad offensive against rebel-held parts of the central city on Tuesday, "is progressing daily by capturing buildings and tightening the noose around the terrorist groups," the security source said.
Syrian authorities refer to all those seeking the ouster of President Bashar al-Assad as "terrorists."
The source added that regime forces had seized a church in the Old City.
Rami Abdel Rahman, director of the Syrian Observatory for Human Rights, confirmed the army had "advanced," adding that troops were shelling the Bab Hud and Wadi al-Sayeh districts.
But he said the army had so far only captured buildings rather than whole streets and fighting was continuing.
"There are street battles, but the loyalist forces are not advancing much because the buildings are mined," said the head of the monitoring group, which collects its information from a network of medics on the ground and opposition activists.
The remaining rebel fighters in Homs "know the area very well and refuse to leave. They want to fight until the end," he added.
On Thursday, members of the UN Security Council expressed concern over the plight of Syrian civilians caught in the renewed fighting in Homs.
And they called for implementation of a resolution passed in February urging immediate access of humanitarian assistance in all parts of Syria.
In February, a UN-led operation evacuated around half of the 3,000 people trapped under army siege in rebel-held parts of Homs city.
But around 1,200 fighters and some 180 civilians are believed to remain in the Old City and surrounding districts.
On Thursday, UN-Arab League envoy Lakhdar Brahimi urged the Syrian government and opposition to resume discussions about lifting the siege on Homs.
"We urge all the parties to return to the negotiating table and complete the deal which was on the verge of being signed," he said.
"It is a matter of deep regret that negotiations were brutally stopped and violence is now rife again when a comprehensive agreement seemed close at hand," Brahimi added.