Violence in Syria has continued despite a UN-backed deadline for a complete withdrawal of troops and weapons coming into effect.
Shelling was reported in Homs early on Tuesday, and there were clashes on the Turkish and Lebanese border overnight.
More than 100 people were killed on Monday, many of them civilians.
Damascus had agreed to the deadline but is demanding written guarantees its opponents will give up arms before ending its military action.
Under the plan - negotiated by the UN and Arab League's special envoy on the Syrian crisis, Kofi Annan - Syrian troops were to begin withdrawing from cities by Tuesday ahead of a full ceasefire coming into place on Thursday.
But Washington said late on Monday there were "no signs yet of the Assad regime abiding by its commitments".
Activists in Syria reported that government troops had been shelling the western city of Homs since early on Tuesday morning, while military activity was reported from other areas.
Turkey has accused Syria of a "clear violation" of its borders, after two shooting incidents left two dead and many injured in Turkey, including Turkish citizens.
Turkey has seen a sharp rise in the number of refugees coming over the border in the past week, and now hosts some 24,000 Syrians, including hundreds of army defectors.
Separately, a Lebanese cameraman was shot dead on Lebanon's northern border with Syria.
After previously agreeing to Mr Annan's plan, on Sunday Damascus called for written guarantees from rebel fighters to end attacks and a promise from foreign states not to fund them.
It said it did not want the rebels to exploit any troop withdrawal to reorganise and rearm themselves.
The Free Syrian Army, the main armed rebel group, said although it backed the truce, it refused to meet the government's new demands.
The BBC's Jim Muir in Beirut says that if there are hopes for salvaging the peace place, they are pinned on Syria's international allies - Russia, China and Iran. They have generally defended the regime, but also support the Annan mission.
Syria's foreign minister is in Moscow for talks in the hope of shoring up support for Damascus, while Mr Anna is travelling to Tehran with the aim of securing Iranian backing for his plan.
The UN says more than 9,000 people have been killed in the uprising against Mr Assad's rule which began more than a year ago.
The Syrian government says 2,000 security personnel have been killed in the uprising and blames the violence on "armed gangs" and "terrorists".