The British-based Syrian Observatory for Human Rights says four women and two children were among the dead.
Eleven people died in the shelling in the village of Mishmishan, according to the group.
An advance party of 16 UN monitors has begun work in the country. This is due to be expanded to 100 by mid-May.
Eventually as many as 300 international peacekeepers are expected to be deployed.
Maj Gen Robert Mood arrived in Syria to take over the observer mission on Sunday.
A cease-fire agreement which came into force on 12 April has helped reduce violence, but fighting is continuing.
UN officials say Syrian government forces are mainly responsible. Maj Gen Mood urged both sides to stop fighting.
The observer mission is part of a plan by the UN's special
envoy Kofi Annan to broker negotiations between President Assad and his
opponents.
Source: BBC News