Troops loyal to President Bashar al-Assad seized several buildings on the edges of rebel-held districts of Homs as they pressed an eight-day assault on the central Syrian city, activists said on Saturday.
The army launched its all-out assault last Saturday, subjecting rebel-held areas to continuous bombardment.
"The most heated battles are taking place on the Khaldiyeh and Bab Hud fronts," Homs-based activist Yazan told AFP via the Internet.
"Starting Friday, regime troops started to advance slowly, seizing several buildings on the edges of Khaldiyeh district," the activist said.
Syria's state news agency SANA said the army captured several buildings in Bab Hud in the city centre.
Rebel-held areas of Homs have been under siege by the regime's military for more than a year.
"The situation is very difficult here. If nothing changes, Homs will fall," Yazan said.
The activist also reported "the collapse of several buildings" because of the shelling, adding that an unknown number of civilians were trapped under the rubble.
Warplanes also launched air raids on the city dubbed "the capital of the revolution" by anti-Assad activists, said the Syrian Observatory for Human Rights.
It reported shelling of the already damaged, landmark mosque of Khaled Ibn al-Waleed.
The Istanbul-based opposition Syrian National Coalition, which on Saturday elected Ahmad Assi Jarba to lead the umbrella movement, urged an immediate international response.
It said this should include "the opening of an emergency humanitarian corridor to remove innocent civilians remaining in the city".
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In protest at the assault, representatives of Homs' opposition city council suspended their membership of the National Coalition.
"We have suspended our membership in the Coalition in protest against the fierce attack against Homs by the Syrian army, Hezbollah and Iran," Coalition member Wasef al-Shemali said.
Lebanese Shiite Hezbollah and the authorities in Tehran are staunch backers of Assad's regime.
"They are using weapons of mass destruction against Homs, while the international community does nothing," Shemali told AFP by telephone.
On Friday Rupert Colville, spokesman for UN High Commissioner for Human Rights Navi Pillay, expressed extreme concern "about the human rights and humanitarian impact" of the regime assault on Homs.
The UN believes some 2,500 to 4,000 people are trapped in the besieged areas, and urges "unrestricted and immediate humanitarian access to all conflict-affected populations in besieged areas".
Elsewhere, warplanes launched air strikes on the outskirts of Damascus as fighting erupted in several flashpoint areas, said the Britain-based Observatory.
Violence has encroached deeper into the capital in the past few months, with several outlying districts battered by shelling and fighting.
Central Damascus is still squarely in army hands.
In Aleppo in northern Syria, large swathes of which are under rebel control, insurgents targeted an area around the feared air force security headquarters, the Observatory said.
The reports come hours after a car bomb in Maaret al-Artik in Aleppo province hit a building used by regime troops, killing and wounding an unknown number, the watchdog said.
More than 100,000 people have been killed in Syria's 27-month war, according to Observatory estimates.
It said that on Friday alone, at least 84 people were killed: 27 civilians, 34 rebels and 23 soldiers.