The White House said Mrs Clinton would carry a message that it was in nobody's interest to see an escalation of the conflict, which flared up a week ago with the assassination by Israel of the leader of the miltiary wing of Hamas, the Islamist group that runs Gaza.
Ban Ki-moon, the United Nations Secretary-General, led a procession of international dignitaries headed for Israel or the Palestinian territories, as the world hoped to grab an opportunity for a quick ceasefire.
Speaking in Cairo, he urged all sides to the Gaza conflict to immediately cease their fire, warning at a press conference in Cairo that an escalation would put the entire region at risk.
"All sides must halt fire immediately," Mr Ban said, as an Israeli military operation against rocket-firing militants in Gaza entered a sixth day, with 109 Palestinians and three Israelis killed.
"Further escalating the situation will put the entire region at risk," he added.
In a sign that Israel was inclined to accept a truce, a senior Israeli official said that after a meeting that lasted most of the night the cabinet had decided to hold off from a threatened ground invasion of Gaza, in order to give Egyptian-led truce efforts a chance to work.
"A decision was taken that for the time being there is a temporary hold on the ground incursion to give diplomacy a chance to succeed," the official told AFP.
Israeli radio reported that Israel wanted to see a 24- to 48-hour truce take effect that could then be used to negotiate the finer details of a full ceasefire agreement.
The Turkish foreign minister and delegates from the Arab League were meanwhile due to visit Gaza, where 11 members of the same family were buried on Monday after their building was flattened by an Israeli F-16 bomb.
Overnight, militants in Gaza fired at least five rockets at the Israeli town of Beersheva. There were no injuries.