Intensified government offensives are widely seen as a bid to strengthen Assad's position before a peace conference proposed by the United States and Russia for next month.
In Brussels, British Foreign Secretary William Hague, who was pushing his European Union colleagues to allow member states to arm the rebels, said the expiry of existing EU sanctions this week meant countries could now choose to send weapons to opposition fighters if they wanted to.
While Britain and France say such a move could strengthen the rebels ahead of the peace talks, other countries oppose sending arms and EU diplomats said there was an agreement not to send weapons for now.
The Syrian military pounded eastern suburbs of Damascus with air strikes and artillery and loud explosions echoed around al-Nabak, 80 km (50 miles) north of the capital, where fighting has cut the highway running north to the central city of Homs, the pro-opposition Syrian Observatory for Human Rights group said.
Opposition activists said Syrian troops backed by Lebanese Hezbollah fighters were pressing a sustained assault on Qusair, a town long used by insurgents as a way station for arms and other supplies from Lebanon.
For Assad, Qusair is a crucial link between Damascus and loyalist strongholds on the Mediterranean coast. Recapturing the town could also sever connections between rebel-held areas in the north and south of Syria.
Hezbollah's deepening involvement in Qusair has raised the prospect of renewed civil war in Lebanon, where two rockets hit the Shi'ite Muslim movement's stronghold in south Beirut on Sunday and one was fired from south Lebanon towards Israel.
The rockets struck hours after Hezbollah leader Sayyed Hassan Nasrallah promised that his anti-Israel guerrillas, fighting alongside Assad's forces, would win whatever the cost.
A Lebanese security source said another 107mm rocket, which did not go off, had been aimed at Beirut airport. The launch sites were near Aitat, in the hills just south of the capital.
U.N. Secretary-General Ban Ki-moon voiced "deep concern" at Hezbollah's admitted combat role and the risk that the Syrian conflict will spill into Lebanon and other neighboring states.
"CHEMICAL ATTACK" AFFECTS DOZENS
The U.S.-Russian initiative so far appears only to have intensified the violence, especially around Qusair and Damascus.
In Harasta, an eastern Damascus suburb largely under rebel control, dozens of people were afflicted by respiratory difficulties after an apparent overnight chemical attack, according to opposition sources. Video showed victims lying on the floor of a room, breathing from oxygen masks.
The sides in the conflict, now in its third year, have accused each other of using chemical weapons. France's Le Monde newspaper published first-hand accounts on Monday of apparent chemical attacks by Assad's forces in April.
The newspaper said one of its photographers had suffered blurred vision and breathing problems for four days after an attack on April 13 on the Jobar front, in central Damascus.
Another video from Harasta overnight showed at least two fighters being put into a van, their eyes watering and struggling to breathe while medics put tubes into their throats.
It was not possible to verify the videos independently.
Syria, which is not a member of the anti-chemical weapons convention, is believed to have one of the world's last remaining stockpiles of undeclared chemical arms.
French Foreign Minister Laurent Fabius told reporters in Brussels there was "increasingly strong evidence of localized use of chemical weapons" in Syria and said Paris would consult its partners on what action ought to be taken.
The U.S.-Russian initiative provides the first slim hope in almost a year for a diplomatic end to a conflict that has cost more than 80,000 lives and caused a refugee exodus that the U.N. refugee agency expects to top 3.5 million by the end of 2013.
After a meeting with U.S. Secretary of State John Kerry in Paris, Russian Foreign Minister Sergei Lavrov said organising a peace conference - which may happen in Geneva in June - was a tricky but not, he hoped, impossible endeavor.
"It's not an easy task. It's a very tall order. But I hope that when the United States and the Russian Federation take this kind of initiative, the chances for success are there," he said after the two met by themselves for roughly 90 minutes.
China, which along with Russia, has three times blocked U.N. Security Council action on Syria, said on Monday it would join the proposed talks and would push all concerned towards peace.
Damascus has indicated it will take part in the talks. But the fractured opposition, which has previously required Assad's exit to be guaranteed before any negotiations, has yet to lay out its position and remains mired in internal quarrels.
The opposition crisis deepened on Monday when liberals were offered only token representation, undermining international efforts to lend the Islamist-dominated alliance greater support.
To the dismay of envoys of Western and Arab nations monitoring four days of opposition talks in Istanbul, the 60-member Syrian National Coalition thwarted a deal to admit a liberal bloc headed by opposition campaigner Michel Kilo.
The failure to broaden the coalition, in which a Qatari-backed bloc influenced by the Muslim Brotherhood is prominent, could sap Saudi support for the revolt.
The coalition's Western backers had wanted more seats for liberals, an idea backed by Saudi Arabia, which had been uneasy about Qatar's rising influence, coalition insiders said.