Sporadic machinegun fire and rocket explosions could be heard in the Baba Amro neighbourhood of the central city which has become a flashpoint of the popular revolt against the regime of President Bashar al-Assad.
Abu Rami, an activist reached by telephone, said the explosions had continued through the night.
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"There are about four blasts every five minutes," he said. "Since this morning the shelling has been concentrated in the neighbourhoods of Baba Amro, Inshaat and Jubar.
"The humanitarian situation is dire. No one can move around. There are snipers everywhere," he added.
Other activists reached by telephone have said food and medicine were in short supply.
The Syrian Observatory for Human Rights said 69 civilians were killed on Monday in Homs and its environs after government troops launched the fiercest assault yet on the town.
The Britain-based group said another 13 died in clashes in the northwestern province of Idlib, one in Aleppo, to the north and 15 near the capital Damascus.
According to rights groups, more than 6,000 people have died since the outbreak of the revolt in Syria mid-March.
