The Hamas-run Palestinian health ministry in Gaza said nine people, including children, had died in the strikes.
In Jerusalem, the rocket fire caused Israel's parliament to be evacuated as sirens sounded.
Tensions between Israel and the Palestinians spiralled in recent days.
Gaza's Hamas rulers had threatened to strike after hundreds of Palestinians were injured in clashes with Israeli police in Jerusalem on Monday.
Israel said it had killed three Hamas militants. "We have started, and I repeat started, to attack military targets in Gaza," Israeli military spokesman Lt Col Jonathan Conricus told reporters.
Hamas sources told the BBC a commander of the Izzedine al-Qassam Brigades, Mohammed Abdullah Fayyad, had been killed.
The past few days have seen the worst violence in Jerusalem for years, with more than 300 Palestinians wounded in confrontations with Israeli police outside the al-Aqsa mosque on Monday.
A planned march by Israeli nationalists which was due to pass through Muslim areas of East Jerusalem's Old City was called off over fears it could stoke unrest.
The Jerusalem Day event marks Israel's capture of East Jerusalem - home to the Old City and its holy sites - in 1967, and usually sees hundreds of flag-waving Israeli youth make their way through the Muslim Quarter via Damascus Gate, chanting and singing patriotic songs.
It is regarded by many Palestinians as a deliberate provocation. This year's march is also taking place in the final days of the Islamic holy month of Ramadan.
The latest violence follows days of clashes between Palestinians and Israeli police in the nearby Sheikh Jarrah district of East Jerusalem, with the possible eviction of Palestinian families from their homes there by Jewish settlers a focal point for Palestinian anger.
Israel's Supreme Court had been due to hold a hearing in the long-running case on Monday, but the session was postponed due to the trouble.