A Palestinian rocket launched from the Gaza Strip killed one person in a city close to Tel Aviv on Thursday, an Israeli emergency official told Army Radio.
At least five other people were wounded in the strike, which hit a four-storey apartment building in Rehovot, the Magen David Adom medical service said.
The latest attack came as Israeli Defence Minister Yoav Gallant told the military to prepare for new operations as well as more rocket fire from the Gaza Strip.
Mr Gallant's comments followed the killing of a senior military leader and two other members of Palestinian Islamic Jihad in a pre-drawn Israeli strike on Gaza on Thursday.
Israel’s military said on Thursday afternoon that it had also killed the deputy head of Islamic Jihad’s rocket operations in a strike on the enclave.
The army said in a statement that Ahmad Abu Daqqa “had a significant part in the rocket launches toward Israel”.
The armed wing of the militant group confirmed that the head of its missile unit, Ali Ghali, also known as Abu Muhammad, had died in the attack.
“Ali Ghali … commander of the rocket launch unit … was assassinated in the south of the Gaza Strip along with other martyrs,” Al Quds Brigades, the armed branch of the group, said.
The Israeli army confirmed it had targeted Ghali in the strike.
Smoke billowed from the densely populated coastal enclave after Israel announced it was targeting the group's rocket launch sites.
Fighting between Israel and militants in Gaza has escalated since Tuesday, with more than 20 Palestinians killed in strikes, including civilians, and hundreds of retaliatory rockets launched.
Warning sirens continued to sound throughout Israel on Thursday morning.
Egypt hosted senior Islamic Jihad official Mohammad Al Hindi in Cairo as part of truce talks to end the flare-up, now in its third day, two faction officials and a foreign diplomat told Reuters.
“Egypt's efforts to calm things down and resume the political process have not yet borne fruit,” Egyptian Foreign Minister Sameh Shoukry told reporters in Berlin.
Officials in the Eshkol Regional Council said that about 10 mortars were launched at towns in their area since Thursday morning.
Israel's military said it believed that at least four Palestinians had been killed in Gaza as a result of failed rocket launches that landed in the enclave.
Far-right Israeli Finance Minister Bezalel Smotrich said on Thursday he would not be opposed to a ceasefire if Islamic Jihad stopped firing at Israel.
Israeli opposition leader Yair Lapid earlier told Israeli radio that his country should “stop now”.
Islamic Jihad said it would end its campaign if Israel agreed to stop killing its militants, which is a sticking point in ceasefire negotiations, according to Mohamad Al Hindi, a senior member of the group.
The group's rocket launch commander Ghali was hiding in a residential complex in Khan Younis when he was killed, the Israeli military said.
Two other militants from the group were killed with him in the air strike.
Ghali led rocket attacks against Israel in recent months.
Israeli Prime Minister Benjamin Netanyahu said Israel had dealt a harsh blow to the militants, warning “this round is not over”.
“We say to the terrorists and those who send them — we see you everywhere. You can't hide, and we choose the place and time to strike you,” he said. Israel would decide when calm is restored, he added.
Egypt, a mediator between the two sides, said it brokered a ceasefire but the efforts appeared to falter as fighting increased on Wednesday with both sides unwilling to back down.
White House National Security Adviser Jake Sullivan emphasised the need to de-escalate tensions during a call with the head of Israel's National Security Council, Tzachi Hanegbi, the White House said on Wednesday.
Mr Sullivan “reaffirmed the administration’s ironclad support for Israel’s security, as well as its right to defend its people from indiscriminate rocket attacks”, according to the statement.
It also noted that Mr Sullivan pushed for “regional efforts to broker a ceasefire, and emphasised the need to de-escalate tensions and prevent further loss of life”.
Earlier, tensions escalated in the occupied West Bank on Wednesday, after Israel carried out arrest raids.
Israeli forces killed two Palestinian in Qabatiya town who they said had fired at them.
In Tubas, an Israeli soldier was wounded in a separate exchange of fire with Palestinian gunmen.
