Palestinian officials, meanwhile, said the key sticking point was the lifting of a five-year blockade on Gaza by Israel, and the opening of the Rafah crossing between Gaza and Egypt. The Hamas leadership also wanted to secure a promise from Israel that none of its political or military leaders would be under threat from targeted assassinations.

Egypt, which has been navigating Morsi’s Muslim Brotherhood’s longtime support of Hamas and its practical interests in stability in the region, had sought to show that while the face of the government had changed, Egypt’s interests and role as a peace broker had not. Successful negotiations also would solidify Morsi’s place as an international leader.

But throughout the week, there have been questions about whether Egypt could lead a deal without U.S. intervention. On Monday, President Barack Obama called Morsi and Netanyahu. Shortly afterward, the White House announced that Clinton would travel to the region immediately. Obama spoke to Morsi for a third time Tuesday, the second call between the two leaders in less than 24 hours.

Earlier Tuesday, Egyptian officials hinted at a possible agreement. As he was leaving his sister’s funeral, Morsi told attendees that "aggression on Gaza will end today and efforts to reach a truce will yield positive results in a few coming hours,” according to the state news service.

Yet soon after Morsi spoke, Israel began dropping leaflets on Gaza urging residents to evacuate to city centers. On Tuesday at least eight people were killed, including two cameramen from the Hamas-owned television station al Aqsa. Sirens sounded across southern Israeli communities as rockets launched by militants in Gaza struck several cities, including the Rishon Lezion suburb of Tel Aviv.

Residents of Israel’s battered south had mixed reactions to talk of a cease-fire.

In Rishon Lezion, the rocket struck a four-story building, injuring several people. It was the first rocket to cause damage in central Israel.

“It just feels so different now knowing that Hamas can reach Tel Aviv,” said Chava Mayiri, a 32-year-old mother of two. “I don’t know what we accomplished in these seven days other than to kill some of their men and to establish that the next time those of us in Tel Aviv have to clean out our bunkers.”

McClatchy special correspondent Amina Ismail contributed to this report.