During her current Middle East tour, Rice stopped briefly in Egypt to discuss the escalation in tensions in the Hamas-controlled Gaza Strip with Egyptian President Hosni Mubarak.
"There has to be an active peace process that can withstand the efforts of rejectionists to keep peace from being made, the people who are firing rockets do not want peace," Rice told a news conference in Cairo.
"They sow instability, that is what Hamas is doing," she said.
Hamas militants have recently intensified rocket and mortar attacks at border towns in southern Israel, including Sderot and Ashkelon. In less than a week of escalating conflict between Israelis and Palestinians 190 Qassam rockets were launched against southern Israel, as well as 20 more powerful missiles and 67 mortars.
Israel responded with airstrikes targeting Hamas facilities and militia, and launched last Wednesday a ground offensive in northern Gaza that killed at least 120 Palestinians, and injured 400, including women and children.
"The rocket attacks against innocent Israelis in their cities need to stop...No Israeli government can tolerate that," she said.
At the same time, she told the Israeli authorities that they needed to be aware of the effects of military operations on innocent people.
On Sunday, Palestinian President Mahmoud Abbas suspended the U.S.-brokered peace negotiations with Israel, demanding an end to the Gaza offensive. The Israeli army pulled out of Gaza on Monday, but Hamas militants continued firing rockets at Israel, prompting additional Israeli airstrikes.
Later this afternoon, Rice headed to the West Bank and Israel to meet Abbas and, separately, Israeli Prime Minister Ehud Olmert in a clear attempt to salvage negotiations, launched at a U.S.-sponsored conference in Annapolis in November.
At the Annapolis forum, Abbas and Olmert pledged to forge a peace deal by the end of 2008.