The fighting comes on the second day of Eid al-Fitr, a major Muslim holiday that marks the end of the fasting month of Ramadan, and a day after the United Nation's new envoy to Syria acknowledged that he had no concrete ideas to end the conflict.
Lakhdar Brahimi also said in a Sunday interview that his mission would be difficult without a unified position by the UN Security Council.
"The problem is not what I can do differently, it is how others are going to behave differently," Brahimi told the Associated Press at his Paris home on Sunday.
"If they spoke in one voice and were clearly supportive of what I will be doing on their behalf, that is what I need," Brahimi said in response to what he wants from the security council.
"Without a unified voice from the security council, I think it will be difficult," Algeria's former foreign minister added.
Monday's violence in Dara'a, birthplace of the country's 18-month-old uprising, was reported by the British-based Syrian Observatory for Human Rights and the Local Coordination committees.
The two groups also reported fighting across much of the rest of the country, with the most intense violence in the suburbs of Damascus and the northern city of Aleppo, with scores killed or wounded.
The reports could not be independently confirmed, but an activist in the Damascus area, El-said Mohammed, said seven people were killed and at least 70 wounded when government forces shelled the town of Moadamiyeh with tanks and mortars. He said the defection on Sunday to the rebels' side of some 30 troops along with a tank from army forces in the area may have been behind Monday's shelling.
Mohammed spoke by Skype from the greater Damascus area. His information could not be verified, but the Observatory said five civilians and three rebels were killed in the shelling in Moadamiyeh.
Brahimi was named on Friday to replace former UN secretary general Kofi Annan as peace envoy to Syria. He served as a UN envoy in Afghanistan and Iraq and helped negotiate the end of Lebanon's civil war as an Arab League envoy.
He said Annan's mission failed "because the international community was not as supportive as he needed them to be".
Russia and China have used their veto power at the Security Council to block strong Western- and Arab-backed action against Syrian President Bashar Assad's regime.
Brahimi was travelling to New York on Sunday. Later he will go to Cairo for meetings with the Arab League. – Sapa-AP