Israeli airstrikes on targets in Gaza continued into the early morning hours of Tuesday, the military said.
The air force bombed a weapons storage facility and two sites where rockets had been launched, according to a statement from the Israel Defense Forces.
A military representative said militants have launched more than 115 rockets toward Israel since Saturday.
"The IDF will not tolerate any attempt to harm Israeli civilians and will operate against anyone who uses terror against the state of Israel," an Israel Defense Forces statement said. "The Hamas terror organization is solely responsible for any terrorist activity emanating from the Gaza Strip."
A Hamas security source told CNN that no casualties were reported after two Israeli warplanes attacked overnight.
Palestinian sources said three rockets had been fired into Israel.
In a CNN exclusive, Israeli President Shimon Peres said Israel should "try to stop" the attacks.
"We don't think we are defenseless," he told CNN's Sara Sidner. "We are restrained. We don't take initiatives. We are careful. We respect human life, and we shall be careful."
But, Peres said, attackers "must understand all mothers want to sleep at night with their babies."
The strikes came a day after Prime Minister Benjamin Netanyahu said Israel is ready to escalate its military response to attacks from Gaza.
"The world must understand that Israel will not sit idly against attempts to harm us. We are ready to intensify the reaction," he said Sunday.
Israeli forces are already striking at terror groups in Gaza that are behind the attacks, he said.
The Palestinian death toll from Sunday's violence was six, according to the Palestinian news agency WAFA. Also, more than 30 Palestinians have been wounded, with 10 of them in critical condition, according to the report.
Initial reports indicate four Israeli civilians were wounded by the rocket attacks, according to Israeli military spokeswoman Avital Leibovich. Four Israeli soldiers were wounded Saturday, according to the military.
"Due to continuous rocket attacks" from Gaza, school was canceled Sunday in some Israeli communities, Leibovich tweeted. She added the hashtag: "#terror."
Hamas spokesman Fawzi Barhoum warned against escalating the violence and targeting civilians, saying "we cannot sit idle towards it. An end should be put to it."