The Israeli military has said it struck Gaza overnight, hours after it intercepted a rocket launched from Gaza and following appeals from the US for all sides to calm escalating violence in Israel and the occupied West Bank.
There were no immediate reports of serious casualties.
The military said its air strikes targeted rocket and weapon production sites used by Hamas, the Islamist group that runs the blockaded strip, in response to yesterday's rocket launch.
Powerful explosions shook buildings and lit up the night sky over Gaza as warning sirens sounded again in Israeli areas around Gaza warning of more incoming rocket fire before dawn.
According to local security sources and witnesses, the first round of strikes - at least seven - hit a training centre of the Ezzedine al-Qassam Brigades, the armed wing of the Palestinian Islamist movement Hamas.
The centre is in the Al-Maghazi refugee camp in the central Gaza.
There was no claim of responsibility for yesterday's rocket from Hamas or the smaller Iran-backed Islamic Jihad movement, which fired rockets at Israel last week.
The armed wing of the leftist Democratic Front for the Liberation of Palestine said it had launched rocket salvos at Israel early today in response to the air strikes and the "systematic aggression" against Palestinian prisoners in Israeli jails.
The exchange of fire underlined the tensions between Israel and the Palestinians after a Palestinian gunman shot dead seven people near a synagogue in East Jerusalem and an Israeli raid in a West Bank refugee camp killed ten Palestinians.
US Secretary of State Antony Blinken urged calm upon wrapping up a visit to the region on Tuesday, in which he reaffirmed Washington's support for a two-state solution to the decades-long conflict.
Top US diplomat for the Middle East, Barbara Leaf, and US special representative for Palestinian affairs, Hady Amr, remained behind to continue de-escalation talks between the sides.
In a tweet sent after yesteday's rocket launch, Israel's far-right National Security Minister Itamar Ben-Gvir, who oversees prisons, said he would push ahead with plans to toughen conditions for Palestinian prisoners.
"The rocket fire from Gaza will not stop me from continuing efforts to cancel summer camp conditions for murderous terrorists," he said, adding that he had asked the security cabinet to convene.
Israel has been carrying out near-daily raids in the West Bank since a spate of deadly attacks by Palestinians in Israel last year, leading to a bloody January for Palestinians in which 35 people, militants and civilians, were killed.