Turkish leaders have appeared to be less receptive to Washington's appeals since a committee of U.S. lawmakers passed the resolution last week labeling as genocide the World War I-era killings of Armenians by the Ottomans - a characterization that Turkey rejects.
The issue raised concerns that, as a result of the resolution, Turkey is more likely to take unilateral military action against rebels in northern Iraq.
"Did they seek permission from anyone when they came from a distance of 10,000 kilometers and hit Iraq?" Prime Minister Recep Tayyip Erdogan said of the U.S. on Friday. "We do not need anyone else's advice."
"If such an option is chosen, whatever its price, it will be paid," Erdogan said, responding to a question about the possible repercussions of a northern Iraq campaign.
Rice, speaking during a visit to Moscow on Saturday, acknowledged that "it's a difficult time for the relationship" between the two allies.
Two senior U.S. officials flew to Ankara from Moscow, where they were on the trip with Rice and U.S. Defense Secretary Robert Gates.
The two are Dan Fried, assistant secretary of state for European affairs, and Eric Edelman, who is the undersecretary of defense for policy and was the United States' ambassador to Turkey from July 2003 to June 2005.
The U.S. House of Representatives' Foreign Affairs Committee approved the nonbinding resolution on Wednesday. Its passage was deemed an insult by most Turks and prompted Turkey to recall its ambassador from Washington for consultations. The resolution could be brought to a vote in the full House by the end of the year.
"Secretary of State Rice Condoleezza Rice asked us before we came here to express that the Bush administration is opposed to this resolution," Edelman told a group of reporters in Ankara after meeting with officials from Turkish Foreign Ministry. NTV television broadcast his remarks with simultaneous Turkish translation. The AP translated them back to English.
The two Americans also wanted to assure Turkey that they will do whatever they can to prevent the genocide resolution from going to a vote in the entire House of Representatives, a U.S. official told The Associated Press. The official declined to be named because of the sensitivity of the matter.
The administration of U.S. President George W. Bush opposed the measure out of concern it would harm relations with an important NATO ally and could generate added danger for U.S. soldiers in Iraq.
At the same time, Turkey, which has long considered a cross-border operation against bases of the Kurdistan Workers' Party in Iraq, has moved more troops and equipment to its side of the border after a recent surge in rebel attacks.
The separatist rebels have been fighting the Turkish government since 1984 in a conflict that has claimed tens of thousands of lives.
Washington opposes any unilateral Turkish action that could destabilize one of the few relatively peaceful parts of Iraq.
A vote in Turkey's parliament authorizing troops to go into Iraq is expected after the weekend. Legislators are expected to vote strongly in favor of action.
The visiting officials presented the U.S. concern with Turkey's military plans.
"Turkish officials told us what has happened in (the province of) Sirnak near the Iraqi border, and we told our concerns" about a military incursion, Edelman said.
The two Americans told reporters they would convey Turkey's unease over rebel activity in Iraqi territory to Iraqi officials. They also said they might return to Turkey for more discussions after the weekend.
Rice said she spoke Friday by telephone with Turkey's president, prime minister and foreign minister about the genocide resolution. "They were dismayed," she said.
In discussing their reaction to the resolution and activities of the Kurdistan Workers' Party in northern Iraq, she said, "I urged restraint."
"The Turkish government, I think, is trying to react responsibly. They recognize how hard we worked to prevent that vote from taking place," the secretary said.