The Local Coordination Committees said in a statement that "seven people were killed on the first day of Eid al-Fitr in Syria, including four in the town of Al-Harra and two in Inkhil, in the Daraa province, and one in the (central) city of Homs."
Daraa is a flashpoint province in southern Syria where pro-democracy protests that have rattled the autocratic regime of President Bashar al-Assad first erupted in mid-March.
The Committees said protesters rallied against the regime after the early morning prayers, that are traditionally held on the first day of Eid al-Fitr, with protests reported in Nawa, Dael and other districts of Daraa.
It said a "huge" protest was formed as worshippers emerged from the Al-Omari mosque in Daraa and marched to the town's cemetery. Muslims traditionally visit their dead on the first day of the feast.
The Committees also reported massive security deployments in the central flashpoint province of Homs, and that gunfire was heard in the vicinity of the citadel of the city of Homs, where communications were largely cut.
On the last day of Ramadan Monday, 17 people were killed by Syrian forces and dozens wounded as troops and security forces conducted raids in several areas across the country, according to the Britain-based Observatory.
More than 2,200 people have been killed in the Syrian regime's crackdown on pro-democracy protests since mid-March, according to United Nations' figures.
The European Union reached an agreement in principle on Monday to ban oil imports from Syria to punish the regime for its crackdown on protesters, diplomats said.
"There is a political consensus on a European embargo of imports of Syrian petroleum products," a diplomat told AFP on condition of anonymity.
The new sanctions were backed by all representatives at a meeting of experts from the 27-nation bloc in Brussels, another diplomat said.
Individual EU governments are expected to give their final approval by the end of the week, the diplomat said.
The Syrian regime, which insists it is confronting "armed terrorist gangs," came under harsh criticism at the weekend from the Arab League, of which it is a member, and from its neighbour Turkey.
On Sunday, the League announced plans to send its chief Nabil al-Arabi to Damascus to help solve the crisis, urging Syria to "follow the way of reason before it is too late."
Washington said Assad is "increasingly isolated" internationally, as a result of the toughening Arab and Turkish positions.