Diplomatic efforts accelerated on Tuesday to end the lethal confrontation between Israel and Palestinian militants in Gaza on one of the most violent days yet in the conflict, as the United States sent Secretary of State Hillary Rodham Clinton to the Middle East and Egypt’s president and his senior aides expressed confidence that a cease-fire was close.

But by late evening there was no announcement, and Mrs. Clinton said she would be working in coming days to complete an agreement. Appearing beside Prime Minister Benjamin Netanyahu of Israel to speak briefly to the press, Mrs. Clinton said she hoped to achieve an end to the hostilities with a deal that moves “toward a comprehensive peace for all people in the region.”

The diplomatic moves to end the nearly week-old crisis came as the antagonists on both sides intensified their attacks before any cease-fire takes effect.