Syrian army forces advanced around rebel-held areas of the Old City of Homs, as a car bomb hit a regime-controlled part of the city, killing 14 people.
Around 1,200 rebel fighters and nearly 200 civilians are believed to be inside the rebel-held parts of the Old City, under army siege for nearly two years.
The army, which began a broad offensive there on Tuesday, "is progressing daily by capturing buildings and tightening the noose around the terrorist groups", a 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.
State news agency SANA said the army had captured buildings in the Bab Hud and Wadi al-Sayeh districts and "killed a number of terrorists in Homs city and around it".
Rami Abdel Rahman, director of the Syrian Observatory for Human Rights, confirmed the advance, saying the army was shelling Bab Hud and Wadi al-Sayeh.
But he said the regime 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.
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The US on Friday described the situation in Homs as "desperate and tragic" and called on the Syrian government to stop attacks in the city.
A State Department statement called for an "end to the barbaric acts committed against civilians".
- 'Violence is rife' -
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.
On Thursday, UN-Arab League envoy Lakhdar Brahimi urged the Syrian government and opposition to resume discussions about lifting the siege.
"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.
On Friday afternoon, state media and the Observatory reported, a car bomb exploded outside a mosque in the government-controlled Homs district of Al-Walid.
State media said it detonated as people were leaving the mosque after weekly Friday prayers.
Meanwhile, in northern Aleppo city, the Observatory said at least 10 people had been killed in shelling and aerial bombardment of rebel-held areas.
At least three children were among those killed, the monitoring group said.
The Syrian regime has waged a campaign of aerial raids including the use of explosives-packed barrel bombs that has prompted an exodus of civilians from rebel-held areas.
In recent days fighting between rebels and regime forces in the city has ramped up, with some 50 combatants from both sides killed in an opposition assault on a military base on an eastern outskirt of Aleppo, according to the Observatory.
And in Mleiha, in Damascus province, the Observatory said at least 15 air raids had been carried out as regime forces backed by fighters from Lebanon's Hezbollah movement battled rebels on the ground.