He said thousands of civilians were trapped in Qusair, including hundreds of wounded. Hezbollah cut off running water when it seized the water station, he said, and food was running out.
The Britain-based Syrian Observatory for Human Rights reported at least three killed in Qusair on Sunday.
The International Committee of the Red Cross and U.N. humanitarian agencies expressed alarm over the fate of thousands of civilians believed trapped in Qusair, including many wounded.
They called on both sides to allow aid to reach civilians, including the wounded. The Red Cross said many of the wounded were not receiving the medical care they need and that food, water and medical supplies were scarce. The U.N. agencies called for an immediate cease-fire to allow civilians to leave the town.
On Sunday, U.N. chief Ban Ki-moon called Syrian Foreign Minister Walid al-Moallem to express concern over the situation in Qusair, according to Syria's state-run news agency SANA.
Al-Moallem told the U.N. chief that the Red Cross and other aid agencies would only be able to enter Qusair until after the end of military operations there, SANA said.
So far, neither side has been able to deliver a decisive blow in Qusair.
A regime victory would solidify Assad's control over the central province of Homs, the linchpin linking the capital Damascus with the Alawite strongholds on the Mediterranean coast. For the rebels, holding the town means protecting their supply line to Lebanon.
The town has become emblematic for the state of Syria's civil war — recent military gains by the regime, but not enough to dislodge the rebels completely, and inaction by a divided international community.
Last month, the U.S. and Russia, who are on opposite sides of the conflict, sought to revive the idea of peace talks between the regime and Syria's political opposition. But prospects for launching talks at an international conference in Geneva began fading after the main Western-backed opposition group said it wouldn't attend as long as Hezbollah fights in Syria and the situation in Qusair remains dire.
Meanwhile, Pope Francis called Sunday for prayers for "beloved Syria" as he spoke to a crowd in St. Peter's Square at the Vatican. He lamented that the war has stricken a defenseless people aspiring to peace, and decried the "plague of kidnappings" in Syria.
Both rebels and pro-regime forces have abducted political foes, members of rival sects and others, including journalists, to settle scores or for ransom. Among those snatched were two Orthodox bishops who were abducted in April. The pope assured families of hostages of his prayers.
Associated Press writers Sarah El Deeb and Yasmine Saker in Beirut contributed to this report.