"Hamas is doing what might be expected, which is using rocket attacks on Israel to arrest a peace process in which they have nothing to gain," Rice said.
"Negotiations ought to resume as soon as possible," she said, adding that any lengthy suspension of talks handed victory to Hamas, which seized control of Gaza last June and whose stepped up rocket attacks into Israel preceded the latest offensive.
Rice's first meeting in Cairo was with Egypt's Foreign Minister Ahmed Aboul Gheit, followed by talks with President Hosni Mubarak.
Experts say Rice faces an uphill battle to revive the peace talks -launched to much fanfare last November, in Annapolis, Maryland with the goal of getting a Palestinian statehood deal before the Bush administration's term ends in January 2009.
"I continue to believe that they can get to a deal by the end of the year if everybody has got the will to do it," said Rice, adding implementation of a deal would take a lot longer.
She dismissed sceptics who have predicted the Annapolis process will fail without including Hamas and that U.S. attempts to isolate Gaza will ultimately backfire.
"It is going to have its ups and downs. There will be good days and bad days and even good weeks and bad weeks. I am going to talk to the parties about staying focused on what needs to be done here," she said.
Rice added the stop in Egypt to her itinerary only in the past few days. Government sources said Rice would be discussing the border during her visits to Egypt, Israel and the PA.
In her talks with Israeli leaders, Rice is expected once again to raise Egypt's request to increase the number of its soldiers on the border by 750.
Rice is also expected to seek Israel's response to the plan to reopen the Rafah crossing into Egypt, and to Fayyad's plan to transfer control of the crossings between Gaza and Israel to the PA.
Olmert to tell Rice: Israel wants to renew talks
Prime Minister Ehud Olmert was set to tell Rice on Tuesday that Israel wants to renew talks with the PA quickly.
Rice, who is due to arrive in Israel on Tuesday afternoon, will head directly for Ramallah for talks with PA President Mahmoud Abbas and Prime Minister Salam Fayyad. She will later dine in Jerusalem with Olmert. Rice will meet with Defense Minister Ehud Barak and Foreign Minister Tzipi Livni on Tuesday.
Rice's visit had been planned to gauge progress on the peace process after President George W. Bush's recent visit to the region. But in light of events in the Gaza Strip, Rice is expected to work toward getting the talks back on track.
Olmert, who is said to have been disappointed in the PA announcement on the suspension of negotiations, will reportedly ask Rice to urge the Palestinians back to the negotiating table.
European Union foreign policy chief Javier Solana, who visited Israel Monday, proposed that the Israelis open a dialogue with Egypt and the PA as soon as possible toward clinching a "package deal" on Gaza.
He said an overall agreement of this type could include new security arrangements on the Philadelphi route, the reopening of the Rafah crossing between the Gaza Strip and Egypt, a solution to the matter of the Israel-Gaza crossings and an attempt to reach a cease-fire with Hamas through Egyptian mediation.
Solana also said that such a dialogue should not be conducted in a way that would be "an achievement for Hamas."
In light of recent calls by some European countries to immediately open the Gaza Strip crossings, Livni told Solana that Europe should not take any action that could be construed as a victory for Hamas. Livni gave a briefing to foreign ambassadors on Monday, telling them that when talking about "collective punishment" it should be remembered that Sderot and Ashkelon are also experiencing collective punishment.