Palestinian medics said at least two people were killed in one of several air strikes in northern Gaza. Residents said Israeli naval boats fired shells from the Mediterranean though none may have hit the strip.
The Palestinian religious affairs ministry said Israeli planes destroyed a mosque. A military spokesman said the army was checking the report.
Sirens sounded in two major southern Israeli cities warning of incoming fire from Gaza. Hamas claimed responsibility for launching rockets.
With no sign of an end to the fighting, casualties spread further afield, with Palestinians reporting 11 killed in the occupied West Bank amid clashes between protesters and Israeli security forces.
At least 128 people have been killed in Gaza since Monday, including 31 children and 20 women, and 950 others wounded, Palestinian medical officials said.
Among eight dead in Israel were a soldier patrolling the Gaza border and six civilians, including two children, Israeli authorities said.
Ahead of a session of the U.N. Security Council on Sunday to discuss the situation, Biden administration envoy Hady Amr, Deputy Assistant Secretary for Israel and Palestinian Affairs, flew in on Friday.
The U.S. Embassy in Israel said the aim was "to reinforce the need to work toward a sustainable calm."
Israel launched day-long attacks on Friday to destroy what it said were several kilometers (miles) of tunnels, launch sites and weapons manufacturing warehouses used by the militants in an effort to halt the rocket attacks.
Across central and southern Israel, from small towns bordering Gaza to metropolitan Tel Aviv and southern Beersheba, people have adjusted to sirens wailing, radio and TV broadcast interruptions and the beeps of cellphones bearing red alerts that send them rushing for cover.
Cross-border hostilities between Israel and Palestinian militants in Gaza have been accompanied by violence in mixed communities of Jews and Arabs in Israel. Synagogues have been attacked and street fights have broken out, prompting Israel's president to warn of civil war.
DIPLOMATIC FLURRY
Egypt was leading regional efforts to secure a ceasefire. Cairo was pushing for both sides to cease fire from midnight on Friday pending further negotiations, two Egyptian security sources said, with Egypt leaning on Hamas and others, including the United States, trying to reach an agreement with Israel.
The foreign ministers of Egypt and Jordan discussed efforts to end the Gaza confrontation and to prevent "provocations" in Jerusalem, Egypt's foreign ministry said.
"The talks have taken a real and serious path on Friday," a Palestinian official said. "The mediators from Egypt, Qatar and the United Nations are stepping up their contacts with all sides in a bid to restore calm, but a deal hasn't yet been reached."
The United Arab Emirates on Friday called for a ceasefire and negotiations while offering condolences to all victims of the fighting, citing the promise of September accords that made the UAE and Bahrain the first Arab states in a quarter century to establish formal ties with Israel.
State news agency WAM quoted Sheikh Abdullah bin Zayed Al Nahyan, the foreign minister, as offering his country's support to bring tensions to an end.
Hamas, the Islamist group that rules Gaza, launched the rocket attacks on Monday, in retaliation for Israeli police clashes with Palestinians near al-Aqsa Mosque, Islam's third holiest site, in East Jerusalem.
The Israeli military said more than 2,000 rockets had been fired from Gaza into Israel since the start of the conflict, around half of them intercepted by missile defence systems and 350 fell into the Gaza Strip.
Civil unrest between Jews and Arabs in Israel itself dealt a strong blow to efforts by Prime Minister Benjamin Netanyahu's opponents to unseat the Israeli leader after a series of inconclusive elections, giving rise to expectations Israelis will go to the polls for an unprecedented fifth time in just over two years.
(Additional reporting by Rami Ayyub, Dan Williams and Ari Rabinovitch in Israel; Ali Sawafta in Ramallah; Aidan Lewis in Cairo, Nandita Bose and Steve Holland in Washington, Michelle Nichols in New York and Emma Farge in Geneva; Writing by Howard Goller; Editing by Daniel Wallis)
