A rocket fired by Gaza militants damaged a synagogue and another hit a kindergarten in the southern Israeli city of Sderot overnight, a military spokeswoman said on Friday.

There were no casualties in the attacks, the spokeswoman said.

"In all, 11 rockets, including a long-range one, and nine mortar rounds were fired towards Israel on Thursday and during the night," she said.

Troops fired at a group of Palestinians in Gaza who had just fired a mortar round on Friday morning, she said, adding that several of the militants were hit.