At a news conference with Mr Abbas, Ms Rice vowed to “redouble” efforts to improve the conditions of the Palestinian people and press Israel to ease the closure of Gaza border crossings.
She later met Israeli Prime Minister Olmert, whose office quoted him as saying Israel planned to open its main commercial crossing with Gaza in the near future.
Israel has frequently closed the Karni gateway, citing security concerns.
Palestinian impasse
Speaking after the talks, Mr Abbas made it clear his patience was wearing thin in efforts to persuade Hamas to ease its policy towards Israel and form a unity government with his Fatah faction.
It’s hoped the power sharing agreement can bring an end to a Western aid embargo.
"If this doesn't happen in the near future, all options are open," said Mr Abbas.
"But the only option I reject is civil war."
So far 14 Palestinians have been killed in fighting between rival factions this week, the worst internal violence in Gaza and the occupied West Bank in a decade.
The most recent victims were two Hamas men ambushed by gunmen in separate incidents today.
Before meeting with Ms Rice, the Palestinian leader said he would use his constitutional powers under Palestinian law at the appropriate time, a clear reference to the possible edict to dismiss the government and to seek new elections.
Fatah argues that Mr Abbas has the right to call early elections under law, but this remains disputed by Hamas.
Ms Rice is on a regional tour partly intended to bolster the moderate Abbas in his power struggle with Hamas. The Islamist group, dedicated to Israel's destruction, defeated Fatah in January elections and formed a government in March.
She said the pair have discussed ways to "make possible a life for the Palestinian people that is not subject to the kind of daily humiliations that we know have been associated with the occupation. That is my program here."