Activists said troops killed nine people and launched assaults on the central cities of Homs and Hama. Among the dead was a man shot dead as he tried to cross the border into Turkey, they said.
The latest bloodshed came as International Committee of the Red Cross (ICRC) head Jakob Kellenberger ended a visit to Syria, where rights groups say 10,000 people have been arrested since anti-regime protests erupted in mid-March.
A senior Arab League official, meanwhile, said secretary general Nabil al-Arabi will visit Damascus on Wednesday carrying an Arab peace initiative for unrest-swept Syria.
The ICRC said Kellenberger met President Bashar al-Assad before winding up his visit and announced that Red Cross delegates visited Damascus central prison in Adra suburb yesterday.
"Initially, we will have access to persons detained by the ministry of the interior, and we are hopeful that we will soon be able to visit all detainees," Kellenberger said in a statement.
"This is an important step forward for our humanitarian activities in Syria," he said.
The ICRC said Kellenberger "welcomed the progress made in terms of access to areas affected by the ongoing violence. He emphasised one of his main concerns now is to ensure that the wounded and sick are able to obtain medical care."