The latest violence comes after 67 people were killed nationwide on Sunday, including 15 in Homs province, the Syrian Observatory for Human Rights said.
"Shelling and shooting renewed in Homs city, with explosions heard in the Khaldiyeh neighbourhood," the Britain-based group said.
It said that four people, including a rebel commander, were killed in an explosion in the town of Mohassan in Deir Ezzor province.
Clashes and shelling also went on through the night in several areas of Damascus province, including the towns of Douma and Qoudsaya, under bombardment by regime forces for the past five days.
The Local Coordination Committees (LCC), made up of opposition activists on the ground, said that Qoudsaya came under "heavy shelling" and that "snipers are shooting at any moving object."
Fares Mohamed, a member of the LCC in Zabadani, a town near Damascus, told AFP via email that the Syrian army has "imposed a suffocating blockade" on the areas around Qoudsaya" and a nearby town.
He said the shelling began after an anti-regime demonstration in Qoudsaya.
The activist added that "huge military reinforcements" had arrived in the town and that the wounded could not be treated due to the intensity of the shelling and sniper fire.
The Observatory reported one person killed in an explosion in Damascus province.
In Douma, a suburb of Damascus, a "tenuous calm prevailed following the bombing of several neighbourhoods and clashes between government forces and rebel fighters at the entrances of the town," the watchdog said.
In the southern province of Daraa, one civilian was reported killed in overnight clashes between rebels and regime troops in the region of Al-Lajat.
Regime forces backed by aircraft overnight also pounded for more than seven hours a region known as the Kurdish Mountain in the northwest province of Latakia, forcing many residents to flee, the Observatory said.
The escalation in violence prompted UN observers at the weekend to suspend their monitoring mission in the country.
More than 14,400 people have died in the 16-month uprising against the regime of President Bashar al-Assad, according to Observatory figures.