Activists say 10 people died early Saturday in the region surrounding Damascus. Activists also warned of fighting in the Latakia region along the Mediterranean coast, but had no information on casualties.
The fighting comes after two explosions rocked Damascus Friday, leaving at least 10 people dead.
A Syrian government newspaper Saturday slammed U.N. Secretary-General Ban Ki-moon, accusing him of encouraging rebel attacks. The Associated Press says the Tishrin newspaper accused the U.N. chief of heaping his criticism on the government and not on rebel forces.
During a news conference in India Friday, the U.N. chief said he was "gravely alarmed" over Syria's rising death toll in spite of the government's repeated commitments to end violence.
The U.N. estimates that more than 9,000 people have been killed in Syria's crackdown on the uprising, while activist groups put the death toll at more than 11,000.
Meanwhile, Lebanese officials said Saturday they intercepted a ship that may have been trying to smuggle weapons to the Syrian rebels.
Officials said the Lutfallah II sailed from Libya and stopped in the Egyptian port of Alexandria before making its way to Tripoli. At least three shipping containers were removed from the ship. Officials said the containers had been loaded with shells, rockets, grenade launchers and other equipment.
Reuters news agency quotes a White House spokesman as saying the United States is "disappointed" about Syria's failure to live up to the peace plan and will continue to "ramp up international pressure" against Syrian President Bashar al-Assad.
European Union Foreign Policy Chief Catherine Ashton expressed concern about Syria's failure to abide by the cease-fire.
Syria has said it will honor the truce and other elements of international envoy Kofi Annan's peace plan for the country, but will respond to attacks by foreign-backed "terrorists" it says are behind the 13-month opposition uprising.
Only a handful of U.N. monitors are currently in the country as part of the cease-fire deal. They deployed Friday to hot spots of violence between government forces and rebels.
Some information for this report was provided by AP, AFP and Reuters.