Israel and Gaza fighters traded heavy fire on Friday but Egyptian mediators launched a new bid to end days of fighting that has killed dozens, all but one of them Palestinian.
The violence has been met with international calls for de-escalation, with the European Union pushing for an "immediate comprehensive ceasefire".
Israel announced it was "striking Islamic Jihad targets" in the densely populated Palestinian territory, while AFP journalists saw air strikes hit Gaza City.
Sirens warning of incoming fire meanwhile rang out in Israeli communities close to the border with the Gaza Strip, as well as in an Israeli settlement near Jerusalem in the occupied West Bank.
Violence broke out Tuesday when Israel killed three top members of the Islamic Jihad militant group, while subsequent strikes have killed at least three other senior figures.
A high-ranking commander, Iyad al-Hassani, was killed in a strike on a Gaza City apartment Friday, a spokesman for the group told AFP.
Hours earlier, Islamic Jihad said the latest rocket fire was a "response to the assassinations and the continued aggression against the Palestinian people".
The launches, witnessed by AFP journalists, came after a rocket killed one civilian in the central Israeli city of Rehovot on Thursday night.
At least 33 Palestinians have been killed, according to Gaza's health ministry, including militants but also children.
Daily life in the coastal territory, ruled by the Hamas militant group, has largely come to a standstill, while Israel has told its citizens near Gaza to stay close to bomb shelters.
In Gaza's central Deir al-Balah area, farmer Belal Basher stood beside the ruins of the home he said was hit by multiple Israeli strikes.
"Our situation is the same as that of any Palestinian citizen whose house is targeted and whose dream, built over the years, is destroyed," the 33-year-old told AFP.
Earlier, there had been cautious optimism a truce may be nearing, with an Islamic Jihad source saying a deal drawn up by Cairo had been circulated among the group's leadership.
But the source subsequently said Israel was "disrupting Egypt's efforts for a ceasefire".
Late Friday, a Palestinian source said Egypt had circulated a new ceasefire formula. "The Palestinian side is going to study it," the source said, adding that Egypt was also waiting for Israel's response.
Israeli public television meanwhile said an "improved" Egyptian ceasefire proposal had been handed to Israel.
The decision to renew air strikes on Gaza this week was authorised by Israeli Prime Minister Benjamin Netanyahu, who returned to power in December alongside extreme-right and ultra-Orthodox Jewish allies.
The violence has wounded more than 110 people in Gaza, according to the latest health ministry toll.
Israel's Magen David Adom emergency service has treated five people who were hit by shrapnel or glass, or suffered blast injuries from the rocket fire.
In Rehovot, 82-year-old resident Ran Lev said he was heading to the bomb shelter when the rocket which killed his neighbour hit.
"The entire apartment was seriously shaking. All the photo frames fell," he said.
The United States, which along with the European Union has blacklisted Islamic Jihad and Hamas as terrorist groups, urged that steps be "taken to ensure that violence is reduced".
Morocco, which normalised relations with Israel in 2020, said it nonetheless "firmly condemns recent Israeli attacks on the Gaza Strip, which have left numerous casualties among innocent civilians," a foreign ministry source said.
In a televised address the leader of Lebanon's Iran-backed Hezbollah movement, Hassan Nasrallah, said the movement was in touch with the Palestinian factions and stood ready to "provide all possible assistance within certain limits".
"But if at any time the responsibility falls to us to take any step or steps, we will not hesitate," Nasrallah said.
In April, Palestinian militants based in southern Lebanon, a Hezbollah stronghold, fired more than 30 rockets into Israel after clashes inside Jerusalem's flashpoint Al-Aqsa mosque.
The Israeli military said it has hit 170 Islamic Jihad targets this week, while more than 860 rockets have been fired from Gaza.
Israel said a quarter of the rockets struck inside Gaza and killed four people, three of them children, an accusation Islamic Jihad and Hamas did not respond to when approached by AFP.
This week's escalation is the worst since August, when 49 Gazans were killed in three days of fighting between Islamic Jihad and Israel.
That conflict followed multiple wars fought between Israel and Hamas since the group took control of Gaza in 2007.