Sirens have been heard in southern and central Israel, with people in Tel Aviv also saying they could hear booms.
At least 12 people have died, including a senior member of the Palestinian Islamic Jihad (PIJ), as a result of Israeli airstrikes, officials have said.
A blast was heard in Gaza City on Friday and smoke was seen coming from the seventh floor of a tall building.
The PIJ said it had responded by firing more than 100 rockets toward Israeli cities, including Tel Aviv.
TV stations appeared to show a number of missiles being shot down by air defense systems, with no reports of casualties.
The Palestinian Health Ministry said that 84 people were wounded, with a senior Islamic Jihad commander, a 23-year-old woman, and a five-year-old girl among the dead.
The strike comes after days of tensions following the arrest of a senior militant in the occupied West Bank on Monday.