Rice met Costas Karamanlis, the Greek prime minister, and Dora Bakoyanni, her Greek counterpart, on Tuesday as part of a five-day trip to Europe that includes Turkey and Bulgaria.
Bakoyanni was noncommittal on Greece's stance, as a non-voting Security Council member, in a possible vote on sanctions against Iran.
"We believe there must be co-ordination within the European Union, and decisions will be taken within the framework of the Security Council," Bakoyanni said.
"We are in the middle of a diplomatic effort, which still has tools at its disposal that allow it to be effective."
As anti-American riots raged near her ministry, Bakoyannis said Iran had to provide "sufficient assurances" that it would not pursue a military nuclear programme.
Riot squads fired tear gas at masked youths hurling petrol bombs and rocks after they tried to break through a police cordon to reach the building where Rice was meeting with Bakoyannis.
The youths set fire to a delivery van and smashed store fronts in one of Athens' premier shopping areas as they were chased by police away from central Syntagma Square.
Protesters tried to break through
a police cordon
The violence and more than a dozen tear gas canisters fired by police led to the breakup of a demonstration by about 4,000 people who had gathered in two rallies.
One had been organised by the Communist Party and another by anti-globalisation activists.
"This is an anti-war rally," said protester Panayiotis Hiundis, 26, a schoolteacher.
"We are not protesting just against Rice, but the imperialist, war-mongering US government."
Bakoyannis and Rice also on Tuesday denied they had discussed the possible use by the US of a large military base on the Greek island of Crete.
"The agenda is to reinforce our diplomatic efforts," Rice said. "I most certainly did not raise facilities for anything, because that is not on the agenda."
Asked about any possibility of US military action to deter Iran, Rice repeated the standard White House reply.
"The United States president doesn't take any options off the table, but we are on a diplomatic agenda here," she said.
The US and European allies are expected to press for binding measures when the UN Security Council begins the next round of its review of the Iranian case as soon as next week.
"The United States president doesn't take any options off the table, but we are on a diplomatic agenda here"
US Secretary of State
Although Rice has recently raised the likelihood of pressing for sanctions, she did not go that far on Tuesday when taking questions following her meeting with Bakoyannis.
Rice and Bakoyannis discussed the future of the war-divided island of Cyprus, but there were no indications that the US would try to broker a deal.
A UN-backed proposal to unify the island fell apart after Greek Cypriots rejected a referendum two years ago.
Rice said Kofi Annan, the UN secretary-general, and others want to be sure any new deal has support before moving ahead.
Rice briefly met with Costas Caramanlis, the Greek prime minister, before she left for Turkey.
Rice said the next step in the international effort to counter Iranian nuclear ambitions is not certain.