Speaking in Moscow on October 13, Rice appealed for restraint against Kurdish rebels in northern Iraq.
Ambassador Recalled
Rice also called for restraint in Turkey's response to a vote by a U.S. congressional panel describing the massacre of Armenians during World War I as genocide.
Washington has warned that any such incursion would further destabilize the situation in Iraq.
Turkey has recalled its U.S. ambassador for consultations after the Foreign Affairs Committee of the U.S. House of Representatives voted on October 10 to approve the nonbinding resolution.
The move came as the Turkish government is expected next week to formally seek parliament approval for an operation against Kurdistan Workers Party (PKK) militants in northern Iraq.
Seeking Cooperation
In a telephone interview with RFE/RL's Afghan Service on October 12, U.S. Ambassador to the United Nations Zalmay Khalilzad said cooperation is key to resolving the issue.
"There has to be a solution to the presence of terrorists elements, including the PKK, in those areas [in northern Iraq]," he said. "The best way to deal with this is through cooperation with the Iraqi [central authorities], and the regional authorities in the Kurdish region of Iraq, and with Turkey."
On the controversial congressional resolution, Khalilzad said the U.S.-Turkey strategic alliance should not be undermined at any price.
"I hope that we deal with this issue -- and the [U.S.] administration has clearly taken a position against the passage of the resolution that is being debated in Congress -- that Turkey and the United States can sustain the strategic alliance, close cooperation, and the kind of closeness that has served both countries quite well in the Cold War and during the period after the end of the Cold War," he said.
Resolution Hurting Relations
The resolution is now likely to be sent on to a vote in the Democratic-led lower house, where a majority has already signed on to the resolution. A parallel measure is in the Senate legislative pipeline.
Turkey has said bilateral relations are in danger over the adoption of the measure.
In Ankara on October 13, Assistant Secretary of State for European Affairs Dan Fried promised the U.S. administration will do "everything" it can to work to prevent the adoption of the resolution.
During meetings with Turkish officials, Fried and Undersecretary of Defense for Policy Eric Edelman expressed "concern" over the possibility of a Turkish military offensive in northern Iraq and promised to convey Turkey's concerns about PKK fighters to Iraqi officials in the Kurdish region.
Washington has warned that any such incursion would further destabilize the situation in Iraq.