Rice stressed the importance of continued efforts to advance a lasting peace between Israel and the Palestinians.
"There's simply no reason to avoid the subject of how we get to a Palestinian state," Rice said after the meeting of the Quartet foreign ministers, held at the US state department.
"We expressed our concern about events on the ground in the Palestinian territories. Obviously innocent people are being caught up in this violence, and it needs to stop"
Condoleezza Rice, US Secretary of State
Sergei Lavrov, Russia's foreign minister, said that "Syria could play a constructive role" in advancing a lasting peace between Israel and the Palestinians.
However, Rice played down such a prospect.
"I hope that [Syria] will in fact try and play a positive role rather than a negative one," she said.
The Bush administration has resisted expanding diplomatic ties with Syria, which it blames for supporting groups such as Hezbollah in Lebanon and Hamas in the Palestinian territories.
Speaking on the violence that swept across Gaza on Friday, Rice said: "We expressed our concern about events on the ground in the Palestinian territories. Obviously innocent people are being caught up in this violence, and it needs to stop.
"The Palestinian people have waited a long time for a state and the Israeli people have waited a long time for the peace and security that would come from having a democratic neighbour."
Peace process conditions
The leaders reaffirmed a statement they signed a year ago, days after Hamas won a surprise victory in Palestinian elections, setting forth the conditions for the peace process.
Hamas has refused to meet those terms, leading to the severance of direct international aid to the Palestinian territories.
"It is pitiful to witness the bloody scenes in Gaza between the brothers"
Later on Friday, the Quartet was condemned by the Hamas-led Palestinian government, which accused it of doing Washington's bidding.
"This position does not contribute to bringing security, stability and calm in the region, but it contributes to increasing the suffering of the Palestinian people," the Palestinian foreign ministry said in a statement.
"The results of the meeting were a complete match to the American position, which imposed a siege against our people. The results were disappointing to our people."