Hamas has agreed with other Palestinian groups to stop firing rockets into Israel, providing Israeli forces stop targeting Gaza.
The move was announced after a meeting between Hamas leaders and insurgent groups.
In the past week at least 10 Palestinians, including several civilians and children, have been killed by Israeli attacks.
In the same period, 80 rockets and mortar shells have been fired into Israel.
Hamas earlier pledged to try to restore a ceasefire that ended on 16 March. There has been no comment yet from Israel on the offer.
On Wednesday, a bomb at a bus stop in Jerusalem killed one person and wounded many others.
The BBC reports the trouble is the most serious since the end of Operation Cast Lead - an Israeli offensive more than two years ago when more than 1300 Palestinians were killed.