Rice blamed Palestinian Hamas radicals for provoking an Israeli military onslaught in the Gaza Strip. The campaign has derailed an already troubled U.S-backed drive for peace terms this year.
"Negotiations are going to have to be able to withstand the efforts of rejectionists to upset them, to create chaos and violence, so that people react by deciding not to negotiate," Rice said in Egypt at the start of two days of efforts to rescue negotiations. "That's the game of those who don't want to see a Palestinian state established."
The moderate, U.S.-backed Palestinian leadership in the West Bank suspended peace talks in protest after an Israeli military offensive that killed more than 100 Palestinians in Gaza. That made restoring two-way talks Rice's chief objective for a trip she had planned to check up on the negotiators' progress.
Rice, who later appeared with Palestinian President Mahmoud Abbas, said that walking away from talks plays into the hands of militants.
"I know that there is great will to try and get to a solution by the end of the year. What we are trying to achieve is not easy ... but I do believe it can be done. We need very much for everybody to be focused on peace," Rice said later Tuesday during a joint press conference with Abbas.
Referring to the opponents of peace, she said, "We won't let them win." Rice also said that Israel should make "a very strong effort to spare innocent life" in Gaza.
For his part, Abbas declared that peace is his first choice in the Mideast.
"I call on the Israeli government to halt its aggression so the necessary environment can be created to make negotiations succeed, for us and for them, to reach the shores of peace in 2008," Abbas said. He was referring to the goal - stated at a U.S.-sponsored Mideast peace conference in November - of reaching an Israeli-Palestinian peace treaty by the end of the year.
Also Tuesday, President Bush said he remains optimistic there will be a Mideast deal by the end of his presidency. Mr. Bush made the remarks in the Oval Office after meeting with Jordan's King Abdullah II.
Mr. Bush said it is "a process that always two steps forward and one step back" and said that people need to make sure that it's just "one step back."
Israel launched the offensive to stop rocket attacks by the Hamas militant groups on nearby Israeli cities, but the assault prompted Abbas to suspend negotiations. Israeli aircraft sent more missiles crashing into Gaza on Tuesday after more rockets were fired on the southern town of Sderot.
Rice backed Israel's right to respond to the rocket fire, but said it must avoid causing civilian casualties.
"The rocket attacks against innocent Israelis in their cities need to stop. This can't go on. No Israeli government can tolerate that," she said. But the Israelis "need to be aware of the effects of these operations on innocent people."
She said Hamas, which took over the Gaza Strip last July, is armed "in part" by Iran and underlined the need for the United States and the West to train and develop the Palestinian security forces loyal to Abbas, whose government controls the West Bank.
"Hamas gets armed by the Iranians and if nobody helps to improve the security capabilities of the legitimate Palestinian Authority security forces. That's not a very good situation," she said at a news conference with Egyptian Foreign Minister Ahmed Aboul Gheit.
Rice said she still thinks the two sides can reach a deal for Palestinian statehood this year.
"I do think that negotiations ought to resume as soon as possible," Rice told reporters Monday on her way to the Middle East. "I understand that the situation has been complicated. But the longer the negotiations are not ongoing or the longer that they are suspended, if that's what one wants to call it, the more it is a victory for those who don't want to see a two-state solution."
Rice declined to call for a cease-fire, which many Israelis think would legitimize Hamas and its hold in Gaza. The Mediterranean coastal strip is the smaller, poorer of two Arab tracts that would form an independent Palestinian state alongside Israel.
Gheit, whose country has sought to isolate Hamas, also stopped short of calling for a cease-fire. He said Egypt was seeking to convince Israel "not to resort to excessive use of force.... The imbalance of power (between Hamas and the Israelis) must be taken into account." He said Egypt also urges the Palestinians to halt rocket fire.
Israel said it wants to continue negotiations, but suggested it also may launch a full-scale re-invasion of the Gaza territory it abandoned three years ago in a first step toward ending defensive occupation of lands the Palestinians claim for the state.
Israel said it would return to Hamas-ruled Gaza if necessary.
"We cannot afford this kind of extreme Islamic state controlled by Hamas," Foreign Minister Tzipi Livni told foreign diplomats in a meeting, according to a ministry statement released Tuesday. Israel evacuated Gaza "not in order to come back, but we might find ourselves in a situation that we have no other alternative."
In Egypt, Rice asked President Hosni Mubarak and other officials for help controlling Gaza's small border with Egypt, site of a border breach in January that became something of a public relations coup for Hamas. Some Israeli military analysts think the more sophisticated longer-range rockets fired at the Israeli city of Ashkelon in recent days probably came into Gaza during the week that fences with Egypt were down.
Rice was also looking for ways to speed aid into Gaza, sealed off for months as Israel tries to punish Hamas and break its rule. She said proposals from Egypt and the Palestinians to reopen a monitored border crossing point have merit.
Gaza and the Palestinian leadership split that underlies the crisis are the largest potential deal-killers for President Bush's goal to sign a peace treaty before the close of his term in January.