Syrian troops and pro-regime militiamen fought their way into rebel-held neighbourhoods of the central city of Homs on Tuesday after besieging them for nearly two years.
Meanwhile, rebels elsewhere in the country have received for the first time at least 20 US-made TOW anti-tank missiles from a "Western source", a rebel official said.
The assault on Homs comes a day after the army recaptured the Christian town of Maalula in the strategic Qalamun region and as state media reported the country would soon move into election mode.
It follows a UN operation to evacuate some 1,400 people trapped inside army-besieged neighbourhoods of Homs in February.
Around 1,300 people, mostly fighters, remained behind.
France will table a proposal before the United Nations Security Council authorising the International Criminal Court to investigate crimes against humanity in Syria, French ambassador to the UN Gerard Araud said on Tuesday.
Araud told reporters that France hoped to introduce the resolution in the next few weeks, following a presentation to council members of a gruesome dossier containing thousands of photos showing detainees who had been starved or tortured in prisons run by the Syrian regime.
Any resolution introduced by France is almost certain to be vetoed by Syria's ally Russia as well as China.
Western diplomats, however, say even in the event of a Russian veto, the measure would continue to pile pressure on Damascus while accentuating Russia's isolation on the council.
Syrian state television reported that the army and the pro-regime militia National Defence Forces (NDF) "have achieved key successes in the Old City of Homs".
Troops were advancing in several neighbourhoods and had "killed a number of terrorists", it said, using the regime's term for rebels.
Local activists and the Syrian Observatory for Human Rights confirmed the operation.
A trapped activist, Abu Fehmi, said the army was "bombing very, very intensely".
Britain-based Observatory director Rami Abdel Rahman said regime forces began the advance a day earlier after NDF forces were deployed to strengthen the regime troops' presence.
Homs is Syria's third city and activists have long referred to it as the "capital of the revolution" because of the huge pro-democracy protests held there when the uprising began in March 2011.
Most of the central city is now under regime control. Rebel-held pockets have been under a siege for nearly two years, leading to dwindling food and medical supplies.
400 still held
Activists said they fear that 400 men, including rebels and draft evaders from Homs who had recently surrendered, may be held indefinitely.
With fighting uninterrupted, state media and the Observatory said a child was killed and at least 40 people wounded in mortar fire on Damascus.
Meanwhile, a rebel official said "moderate, well-organised fighters from the Hazm movement have for the first time received more than 20 TOW anti-tank missiles from a Western source", without specifying who had supplied them.
The Hazm movement, part of the opposition Free Syrian Army, brings together mainly ex-army officers and soldiers who defected from the military.
"Dozens of fighters have been trained with international assistance in the use of these missiles," the rebel source said, adding that the weapons have been used in flashpoint areas of Idlib, Aleppo and Latakia provinces in the north.
Vastly outgunned by the army, rebels have frequently called on the West to provide them with specialised weaponry.
Western supporters of the revolt have hesitated to arm the rebels for fear weapons may fall into the hands of powerful jihadist groups.
Meanwhile, Al-Watan daily said the speaker of parliament would announce next week a date for presidential elections.
They are likely to be held in June. Assad, whose seven-year term expires on July 17, is expected to run and win.
Electoral rules require candidates to have spent the past 10 years in Syria, effectively preventing the exiled opposition from competing.
It remains unclear how the government can hold elections with much of Syria under rebel control and nearly half of its population displaced.