US Secretary of State Condoleezza Rice has held talks with Egyptian officials, the first stage of a trip aimed at saving Israeli-Palestinian peace talks.
Palestinian leader Mahmoud Abbas broke off contacts with Israel in protest at its recent offensive in Gaza, which has left more than 110 Palestinians dead.
Ms Rice said the US was concerned about the toll of innocent life, but blamed Hamas for triggering the bloodshed.
She said talks must not be sabotaged by those rejecting a peace deal.
Ms Rice headed on to Israel and the West Bank for further negotiations with Israeli and Palestinian leaders.
Israel has now pulled its troops out of Gaza, which is under control of the militant Hamas group, but has warned of fresh action to prevent militants firing rockets at populated areas in southern Israel.
"There has to be an active peace process that can withstand the efforts of rejectionists to keep peace from being made," Mr Rice told reporters in Cairo.
"The people who are firing rockets do not want peace, they sow instability, that is what Hamas is doing," Ms Rice said.
Effects on innocent
On Tuesday, a rocket from Gaza hit the nearby Israeli town of Sderot, causing extensive damage.
Israeli forces launched several air and ground strikes on rocket squads and Hamas installations, killing at least two militants.
Parts of Jabaliya, Gaza, have been destroyed by the operation
Three Israelis have died in recent days - a civilian killed by a rocket and two soldiers in the Gaza clashes.
Human rights groups say about half of the approximately 115 Palestinian fatalities have been civilians, and Israel has been accused of a disproportionate military response in breach of the laws of war.
"I have told the Israelis that when they are engaged in defending themselves they need to be aware of the effects of those operations on innocent people... and what can happen the next day," Ms Rice said in Cairo.
She was speaking after meetings with President Hosni Mubarak, as well as the prime minister and the influential intelligence chief Omar Suleiman.
In her statements, she stressed US commitment to the Annapolis process launched in November, which envisages a newly-founded Palestinian state existing side-by-side with Israel.
She said the way to reach that was through negotiations, improving humanitarian conditions for Palestinian and progress in each sides implementation of the international peace plan known as the roadmap.
Hamas repeated its accusation that the US administration was giving Israel a green light to "massacre" Palestinians in Gaza.
"[Mr Abbas] must put an end to the negotiations and not to content himself with suspending them," said Hamas spokesman Sami Abu.
The violence in Gaza has transformed Ms Rice's trip to the region. She had hoped to be nudging Israel and Mr Abbas towards progress in peace talks, but is now attempting a rescue mission to prevent them from completely collapsing.
Israel and the West have shunned Hamas over its refusal to recognise Israel and opposition to the peace process. Hamas ousted Mr Abbas's forces from Gaza in June, but he remains in control of Palestinian-administered parts of the West Bank.
The Gaza conflict has sparked violence in the Israeli-occupied West Bank, where a Palestinian teenager was shot dead by a settler near a Jewish settlement on Monday.
Palestinian security said he was with a group of Palestinian youths who planned to throw rocks at the settlement. The settler was arrested by Israeli police but later released.
"The family of the victim refused to release his body for an autopsy and therefore we could not establish the responsibility of the Israeli implicated in this affair," said a police spokesmen.
Extra Israeli police and troops were stationed in East Jerusalem and the West Bank to prevent a repeat of Monday's rioting.