Rice said if Iranian nuclear negotiator Ali Larijani agreed to a suspension of processing uranium "we would be on a course for negotiations."
But, Rice told reporters, she had told Solana "clearly this won't go on very much longer."
"I did wish Solana well, and we are all awaiting the outcome of these discussions," she said while welcoming Foreign Minister Dora Bakoyannis of Greece to her office for talks.
Rice said the U.N. Security Council had established a "pathway" to sanctions against Iran unless it decides to suspend its enrichment and reprocessing of uranium.
The Greek foreign minister, whose government is currently president of the council, said "we are waiting to see how the negotiations are going" before deciding on sanctions.
"When we have the result then we come back and have our discussions about that," she said.
Earlier, State Department spokesman Sean McCormack said whether Iran was agreeable to a temporary and verifiable suspension would not be known until Solana concludes his meetings with Larijani.
"It may require several meetings to find out," the spokesman said. "There may be an opportunity here," he said.
While Iran may be playing for time, he said, the United States and other governments were in agreement on holding off on U.N. sanctions against Iran for a while if there is a chance for a diplomatic resolution of the long-running dispute over Iran's nuclear programs.
"There may be an opportunity here, there may be a little opening if we just give the Iranians a little time and space,"McCormack said. "Perhaps they will come through with a positive answer."
Senior administration officials warned Iran after it did not meet an Aug. 31 deadline to suspend uranium enrichment that the United States would seek sanctions against Iran in the U.N. Security Council, possibly by the end of September. But so far, the United States has been short of the council votes that would be needed to impose sanctions on Tehran.
McCormack said Wednesday that Solana saw an "opportunity" in his meeting with Larijani "if we give the Iranians a little time and space."
"We want to give that every opportunity to succeed," he said.
The administration's sanctions strategy is to impose a series of increasingly potent penalties against Iran, beginning with curbs on technology that could be used in military programs.
The United States and the European Union contend Iran is trying to build nuclear weapons. Iran disputes the accusation and says it is merely seeking more energy with its nuclear work.