Israeli prime minister said they are still in the midst of the campaign and fiercely attacking the Gaza Strip.
Egypt has been trying to facilitate a ceasefire, an effort confirmed by Hamas and Islamic militia officials.
Both Hamas and Islamic militias are considered terrorist groups by Israel and the US.
Israel and Gaza militants traded more heavy fire early Thursday, the third day of the worst escalation of violence since the middle of last year over the Palestinian coastal enclave.
Air strikes and missiles from Israel have killed 25 Palestinians since Tuesday, said Gaza officials — among them fighters and civilians, including several children.
Early Thursday, shops in Gaza were shuttered and the streets were largely abandoned as Israeli military aircraft circled over the territory where several buildings lay in ruins.
More than 500 rockets have been fired from Gaza at Israel since Tuesday, the army said, with no casualties reported in Israel so far.
Of these, 368 made it over the border and 154 were intercepted by the Iron Dome missile defence system, while 110 fell inside Gaza, it said.
The Islamic militant group told AFP that rockets were fired again at Israel around 9:00 am (0600 GMT) and confirmed it had lost four military leaders in strikes in recent days, the most recent being Ali Ghali, commander of a rocket launch unit.
Another militant group, the Popular Front for the Liberation of Palestine, said that four of its fighters had been killed.
Still in the midst of campaign
Israeli Prime Minister Benjamin Netanyahu said in a TV address late Wednesday that they are still in the midst of the campaign and fiercely attacking the Gaza Strip.
"We say to the terrorists and the ones sending them: we see you everywhere, you cannot hide, and we choose the place and the time to hit you," Netanyahu added.
"We hope that the wave of escalation will end, but we support revenge for the martyrs. Israel assassinated a leader in (Islamic) Jihad at dawn today because it does not want calm,” 48-year-old Mamoun Radi said in Gaza City's Al-Rimal District.
Across southern Israel, sirens wailed intermittently through the night and Thursday morning.
Miriam Keren, 78, an Ashkelon resident, said a Gaza rocket had destroyed a workshop and damaged her house.
"All the shrapnel is in the room, the house was shaken very powerfully, the glasses fell, the walls were damaged," she told AFP.
"Luckily I have a safe room and I entered it immediately and closed the door. This isn't the first time the house was hit but I'm not afraid, neither was I yesterday. You're shocked for a moment but it's not about fear. It's more unpleasant, very unpleasant," she added.
“Egypt has been trying to facilitate a ceasefire,” an anonymous Israeli official told AFP, an effort confirmed by Hamas and Islamic militia officials who did not elaborate.
Hamas spokesman Abdul Latif al-Qanou said on Wednesday that the strikes of the unified resistance are part of the process of responding to the massacre committed by Israel.
The Arab League has condemned the barbaric Israeli raids on the Gaza Strip, which targeted civilians, children and women in residential neighbourhoods.
US National Security Advisor Jake Sullivan reaffirmed Washington's ironclad support for Israel's security.
Both Hamas, which rules Gaza, and Islamic militias are considered terrorist groups by Israel and the US.
This week's Gaza clashes are the worst since a three-day escalation in August killed 49 Palestinians, with no Israeli fatalities.
Violence has also flared in the occupied West Bank, where the Israeli army has staged repeated raids against militants which have often flared into street clashes or gun battles.
The conflict has escalated since veteran leader Netanyahu returned to power late last year heading a coalition with extreme right and ultra-Orthodox parties.
Israel has also been shaken by its biggest domestic political crisis in decades as mass protests have flared against plans to reform the justice system, spearheaded by Netanyahu who is also battling corruption charges in court.