About 50 mortars were fired – two Israelis were hurt, Israel says.
Israeli tanks later shelled targets in the coastal strip, wounding at least five people, Palestinian officials say.
The Islamist group Hamas, which runs Gaza, said it fired some of the mortars. Three days ago an Israeli air strike killed two of its members.
The BBC’s Jon Donnison in Gaza says this seems to be an escalation – both in terms of the number of rockets fired from Gaza and the fact that Hamas said it was responsible.
Hamas’s military wing said it launched dozens of rockets, our correspondent reports.
Hamas and Israel have largely halted hostilities since the end of the Gaza war in January 2009, but skirmishes often break out around the border area.
Although members of Hamas’s military wing rarely carry out attacks, the Israeli military says it holds the group responsible for all militant activity in the Gaza Strip.