The attacks early on Thursday come in the wake of a deadly Israeli raid in the occupied West Bank city of Jenin last week.
The raid, in which ten Palestinians were killed, was followed by Palestinian attacks targeting Israelis over the weekend, including a shooting in occupied East Jerusalem in which eight Israelis were killed.
The unrest has also triggered exchanges of fire between Israeli forces and Palestinian groups in Gaza.
This included rockets fired from the blockaded strip on Wednesday night. No Palestinian group has claimed those launches.
The Israeli military said its air raids hit rocket and weapon production sites used by Hamas, the group that governs Gaza.
After the raids, media outlets reported new rounds of rockets fired from Gaza and explosions that shook buildings and lit up the night sky over Gaza.
Air raid sirens meanwhile sounded in Israeli areas. There were no immediate reports of serious casualties.
The armed unit of the left-wing Democratic Front for the Liberation of Palestine announced it had launched rocket salvos at Israel early on Thursday in response to the air raids and the “systematic aggression” against Palestinian prisoners in Israeli jails.
In a tweet sent after Wednesday’s rocket launch, Israel’s far-right National Security Minister Itamar Ben-Gvir, who oversees prisons, stated 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 continued, adding that he had asked the security cabinet to convene.
Israel’s treatment of Palestinian prisoners has been routinely criticised by human rights organisations, with hundreds held without charge in what Israel calls “administrative detention”.
Israel has been carrying out near-daily raids in the West Bank for a year.
A new far-right Israeli government came into power at the end of last year, and January has been a particularly bloody month for Palestinians, in which 35 people, both fighters and civilians, were killed.
Israeli forces have killed at least 200 Palestinians in the past year.