Syrian government troops fought deadly battles with armed rebels as the European Union urged Russia to overcome differences over Syria to end 15 months of bloodshed.
Activists claimed on June 4 that Syrian rebels killed at least 80 government soldiers over the weekend.
A spokesman for the rebel Free Syrian Army said the rebels were no longer committed to a UN-backed peace plan that has failed to end violence in the country.
While holding talks in St. Petersburg with Russian President Vladimir Putin, EU Council President Herman Van Rompuy said Moscow and the EU "fully agree" that the peace plan brokered by United Nations-Arab league envoy Kofi Annan provides "the best opportunity" to avoid civil war in Syria.
Rompuy said it was essential that the EU and Russia work together to resolve the Syria crisis.
"The European Union and Russia might have some divergent assessments, but we fully agree that the Annan plan, as a whole, provides the best opportunity to break the cycle of violence in Syria, avoiding a civil war, and in finding a peaceful, lasting solution," Van Rompuy said.
"We need to combine our efforts in order for this to happen and to find common messages on which we agree."
The West has criticized Russia's stance on Syria after Moscow refused to back tougher measures against the Syrian government in response to last month's massacre of more than 100 people in the town of Houla.
The UN and Western states have linked pro-government forces to the killing.
Moscow is a longtime ally and weapons supplier to the Syrian regime.
End Of Cease-Fire?
President Bashar al-Assad on June 3 vowed to crush an antiregime uprising after the rebel Free Syrian Army announced that it was resuming "defensive operations."
The British-based Syrian Observatory for Human Rights said on June 4 that rebels had told the group that units operating in the capital, Damascus, and the opposition stronghold province of Idlib had destroyed tanks and killed more than 100 soldiers over the weekend.
The group said it was able to confirm the names of 80 dead through local doctors.
The UN-backed cease-fire has been violated daily since it went into effect on April 12.
But UN Secretary-General Ban Ki-moon on June 4 called the Annan plan "central" to the resolution of the Syrian crisis.
"I'm very much committed to working together with the League of Arab States and joint special envoy Kofi Annan and with the key members of the United Nations to find a solution so that a political dialogue can begin," Ban said.
The Syrian Observatory for Human Rights says as many as 2,400 of the more than 13,500 people the group says were killed since the uprising began have died since the cease-fire went into effect.
With reporting by AFP, AP, and Reuters