Secretary of State John F. Kerry on Tuesday broadened the U.S. effort to reach a cease-fire in Gaza, seeking to revive a truce proposal rejected by Hamas militants a week ago.

Kerry met Tuesday with the intelligence chief of the Palestinian Authority, Majid Faraj, and with Egyptian President Abdel Fatah al-Sissi and other authors of the Egyptian cease-fire proposal.

There was no sign of progress toward reviving the truce offer, or amending it to make it more attractive to Hamas, as the United States is quietly urging. Israel accepted the proposal, but Hamas said it met none of the group’s demands.

“We are continuing to work, and there is more work to be done,” Kerry said after meetings at Egypt’s presidential palace.

The top U.S. diplomat is in the Middle East for open-ended talks aimed at stopping the violence, which has killed about 600 Palestinians, many of them civilians, and 29 Israelis. It is the longest and deadliest episode in the on-again, off-again Israeli-Palestinian conflict since President Obama took office.

The Associated Press reported that before Kerry began his meetings with top Egyptian and Arab League officials Tuesday, Israeli aircraft hit more than 70 targets in the Gaza Strip, according to a Gaza police official. They reportedly included the home of the late leader of Hamas’s military wing, five mosques and a soccer stadium.

Israel has also been targeting an extensive tunnel system along its border with Gaza, and its ground offensive has pressed deep into the Palestinian territory, which is governed by Hamas. The announcement this spring of a Palestinian unity government headed by the moderate Fatah wing and backed by the militant Hamas faction helped sink U.S.-led peace talks with Israel but has had no apparent effect on reining in Hamas or stopping rocket fire from Gaza into Israel.

There was no immediate response from Kerry to reports Tuesday that an Israeli soldier is missing after ground operations in Gaza. “Our thoughts are with his family,” State Department spokeswoman Jen Psaki said, referring inquiries to the Israeli military.

It is not clear that Israel is ready to halt the offensive now, and Hamas has pledged to continue to fight.

Israeli Prime Minister Benjamin Netanyahu has said that he welcomes efforts toward a truce, but he has not publicly invited Kerry to come to Israel. U.S. officials said he may go there later this week but for now is conducting talks from Cairo.

Kerry was deferential to Egypt, stressing that his role is to assist the longtime Arab power broker as it leads the cease-fire efforts.

“There is a framework available to end the violence, and that framework is the Egyptian initiative that has been put forward,” Kerry said as he and Foreign Minister Sameh Shoukry addressed reporters.

Shoukry thanked Kerry for the U.S. backing but stressed that the Egyptian proposal had received “wide support” on its own. The Arab League and the United Nations back the plan.

“We have reached a common vision, which is to push the Palestinians and the Israelis to reach a cease-fire agreement, and to put an end to the bloodshed and the killing of innocent women and children,” Shoukry said.

A senior State Department official later said a truce is not immediately at hand.

“Right now our focus is on stopping the rocket fire so that we can begin a serious negotiation on the key issues,” said the official, who spoke on the condition of anonymity to describe Kerry’s objectives. “There are a range of options under consideration for a cease-fire. We did not expect to resolve that question today.”

Egypt and other Arab states, notably Qatar, are applying pressure on Hamas to relent.

Sissi’s military-backed government came to power after the ouster last year of President Mohamed Morsi, a Muslim Brotherhood stalwart. The new government has banned the Brotherhood, which had close ties to Gaza’s Islamist militants. That limits Cairo’s direct influence over Hamas, but Egyptian and U.S. officials say Egypt’s control of key border crossings with isolated Gaza gives it significant leverage.

The Obama administration is urging greater humanitarian access to Gaza through those border points, which could encourage Hamas to talk, Arab and other officials said.

“Hamas has a fundamental choice to make, and it is a choice that will have a profound impact for the people of Gaza,” Kerry said. “The Egyptians have provided a framework and a forum for them to be able to come to the table to have a serious discussion together with other factions of the Palestinians.”

Kerry’s presence in the region places obvious additional pressure on Israel to halt its offensive, but he was careful Tuesday to defend Israel’s right to prosecute what it calls a defensive military effort.

Growing international criticism of Israel’s two-week-old campaign centers on the heavy civilian death toll and what many consider a disproportionate use of force. Past Israeli-Palestinian conflicts have ended when the United States, as Israel’s chief ally and international defender, leaned on Israel to stop.

Kerry’s visit comes after he was caught on tape Sunday apparently criticizing Israel’s offensive in the Gaza Strip as being far larger than the “pinpoint” operation that Netanyahu had promised.