Local officials in Israel said the rockets landed in open areas, causing no damage or injury, The New York Times reported.
A military official said two rockets were intercepted by Israel's Iron Dome missile defense system.
No injuries were reported in Gaza.
Israeli military leaders said retaliatory airstrikes were carried out against what were identified as weapons storage facilities and a rocket launch site in southern Gaza.
Israeli military spokesman Peter Lerner said in a statement the rocket attacks were "an intolerable act of aggression against Israel and its civilians."
"Hamas is held accountable for all acts of terrorism deriving from the Gaza Strip," Lerner said.
Israeli officials also announced the commercial cargo crossing between Israel and Gaza would be blocked indefinitely because of the rocket fire.
The incident, which began Sunday and broke weeks of relative calm, may have been touched off by an internal dispute in Gaza between Hamas, the Islamic militant group ruling the Strip, and the extremist Islamic Jihad, one of whose members was killed when Hamas police tried to arrest him during the weekend, the Times said.
Raed Jundiyeh, the militant who was killed, was wanted by Hamas in the kidnapping of a Gaza resident and possibly by Israel for his role in rocket attacks, the Times said.
Islamic Jihad militants also claimed Hamas militants raised tensions during Jundiyeh's funeral, the Times said. By Monday, investigations indicated the rocket firings appeared to have been carried out by friends of Jundiyeh.
Putin thinks Obama would save him if he were drowning
Chipotle plans first price increase in 3 years