Official Syrian media said the army was consolidating its grip on Qusayr, a strategic prize in the two-year conflict.
The battle for Qusayr began on Sunday, when regime forces backed by Hezbollah stormed the western town, casting a shadow over US-Russian efforts to organise a peace conference on Syria.
By Monday, the fighting was focused on the east of the town, while thousands of civilians were trapped inside, activists said.
The Syrian Observatory for Human Rights said the fighting had left at least 56 rebels dead, six of them on Monday, and four civilians including a woman.
It also said that "28 members of Hezbollah's elite forces were killed and more than 70 others wounded in clashes in the town of Qusayr yesterday," Sunday.
A source close to Hezbollah told AFP at least 20 members had been killed in Syria fighting alongside President Bashar al-Assad's forces.
A White House statement said Obama "stressed his concern about Hezbollah's active and growing role in Syria, fighting on behalf of the Assad regime, which is counter to the Lebanese government's policies".
Syria's official SANA news agency reported that Syrian troops "are restoring order and security to the eastern part of Qusayr, eliminating terrorists (the regime term for rebels), destroying their dens and defusing bombs near the centre of the town".
An activist on the ground reported intense battles in eastern Qusayr but denied the army had advanced as far as it claimed.
"The army has failed to secure any definitive advance so far. The battles are focused on the east now, where the regime still had a foothold. Now Hezbollah and regime forces are using that foothold to try and break in," Hadi al-Abdallah told AFP via the Internet.
He said at least 25,000 civilians were trapped.
"They have no way of getting out. Trying to get out of Qusayr is a suicide operation," said Abdallah.
He called the latest assault one of the fiercest since the uprising against the Assad's regime erupted in March 2011.
Qusayr is strategic because it sits between Damascus and the coast and is near the Lebanese border.
Violence has frequently spilled over from Syria into Lebanon, where the population is divided over the conflict.
On Monday, a Lebanese soldier was killed in the northern city of Tripoli, as the army tried to quell sectarian clashes between Sunnis who support the Syrian revolt and Alawites who back Assad.
In Doha, Qatar's emir, Sheikh Hamad bin Khalifa al-Thani, lashed out against the international community.
"It is no longer acceptable that influential states in the international community do not act to end the horrific tragedy and escalating humanitarian catastrophe," Sheikh Hamad said.
He lamented the "failure of all international and Arab initiatives to get the Syrian regime to listen to the sound of reason".
Syria's umbrella opposition National Coalition, warning that "a civilian massacre will soon take place", urged the Arab League to convene an emergency meeting of Arab foreign ministers and take measures "to protect Qusayr".
The French foreign ministry urged "all the players in a position to avoid a new massacre of the Syrian civilian population to mobilise without delay".
British Foreign Secretary William Hague said London remains committed to amending the EU arms embargo on Syria, but stressed it had taken no decisions to arm the rebels.
Foreign ministers of the so-called Friends of Syria group of nations are due to meet on Wednesday in Jordan, ahead of a planned Syria peace conference which Washington and Russia are hoping to organise.
On the humanitarian front, aid organisation Oxfam warned that as the hot Middle East summer approaches health risks could increase for hundreds of thousands of Syrian refugees in Jordan and Lebanon.
The UN says that more than 1.5 million Syrians have fled the conflict and estimates that more than 70,000 people have been killed since March 2011.
The Observatory has a higher toll of around 94,000 killed.
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