ASTANA, Kazakhstan — Secretary of State Condoleezza Rice on Sunday rejected any suggestion that U.S. efforts to build closer ties to this former Soviet republic are meant to undermine Russian influence in Central Asia.

"This is not a zero-sum game," she told reporters flying with her to the Kazakh capital. U.S. gains need not mean Russian losses, she said.

"First of all, Kazakhstan is an independent country. It can have friendships with whomever it wishes," she said. "That's perfectly acceptable in the 21st century, so we don't see and don't accept any notion of a special sphere of influence" for Russia in this region.

Later at a joint news conference with her Kazakh counterpart, Foreign Minister Marat Tazhin, Rice said no one should question Kazakhstan's desire to have good relations with all countries in its region.

"This is not some kind of contest for the affection of Kazakhstan," Rice said.

Tazhin described his country's relations with the United States as "stable," and Kazakh relations with Russia as "excellent" and "politically correct." Asked by a reporter whether he considered his country to be in a Russian "sphere of influence," Tazhin said no, adding that he believed such a question was of interest mainly to academics and to journalists.

Rice was meeting later with President Nursultan Nazarbayev and Prime Minister Karim Masimov.

In the interview en route to Astana, Rice disclosed that Deputy Secretary of State John Negroponte was in Iraq this weekend on an unannounced visit to talk to the Iraqi government about planning for the transition period ahead as more U.S. forces withdraw and Iraqis take on more responsibilities.

She said Negroponte also would discuss with Iraqi leaders the remaining obstacles to completing a security agreement that would govern the U.S. military presence in Iraq beyond December, when the current legal authorities expire. Rice said the negotiations "are going along" and are close to being finished.

"We are close, but as you might imagine, because it's an important and difficult agreement when you're trying to work out arrangements that are both going to protect our people and be responsive to Iraqi sovereignty, that just takes time," she said.

Rice said Negroponte is "not doing anything particularly about it" on this visit beyond discussing it with Iraqi leaders. Her characterization of his role did not seem to indicate that he was in Iraq to finalize a deal.