KIEV — The tense Russian-American jockeying over the fate of Ukraine escalated Thursday as a Kremlin official accused Washington of “crudely interfering” in the former Soviet republic, while the Obama administration blamed Moscow for spreading an intercepted private conversation between two US diplomats.

An audiotape of the conversation appeared on the Internet and opened a window into American handling of the political crisis, as the two diplomats candidly discussed the composition of a possible new government to replace the pro-Russian Cabinet of Ukraine’s president, Viktor Yanukovych. It also turned the tables on the Obama administration, which has been under fire lately for spying on foreign leaders.

The developments on the eve of the Winter Olympics opening in Sochi, Russia, underscored the increasingly Cold War-style contest for influence here as East and West vie for the favor of a nation of 45 million with historic ties to Moscow but a deep yearning to join the rest of Europe.

The tit-for-tat has been going on since November, when Yanukovych spurned a trade deal with Europe and accepted a $15 billion loan from Moscow. Months of street protests have threatened his government, and US officials are now trying to broker a settlement — an effort the Kremlin seems determined to block.

The posting of the audiotape represented a striking turn in the situation. It was posted anonymously on YouTube on Tuesday under a Russian headline, “Puppets of Maidan,” a reference to the square in Kiev occupied by protesters, and then tweeted Thursday by a Russian government official who called it “controversial.”

The tape captured a four-minute telephone call on Jan. 25 between Victoria Nuland, the assistant secretary of state for European affairs, and Geoffrey Pyatt, the ambassador to Ukraine, trading their views of the crisis, their assessments of various opposition leaders, and their frustrations with their European counterparts. At one point, Nuland used an expletive to describe what should happen to the EU.

The two were discussing Yanukovych’s offer to bring two opposition leaders, Arseniy P. Yatsenyuk and Vitali Klitschko, into the government as prime minister and deputy prime minister. The two Americans favored Yatsenyuk, a former economics minister, and Nuland said Klitschko, a former world heavyweight boxing champion, should not go into government.

“I don’t think it’s a good idea,” Nuland said.

Pyatt expressed hope for a deal to form a new government but warned that Moscow would try to undo their negotiations.

“If it does gain altitude, the Russians will be working behind the scenes to torpedo it,” he said.

A link to the secret recording was sent out in a Twitter message Thursday by Dmitry Losukov, an aide to Russia’s deputy prime minister, just as Nuland was in Kiev meeting with Yanukovych and opposition leaders. The White House pointed to that as an indication of Russian involvement, although it said it was not accusing Moscow of taping the call.

“I think it says something about Russia’s role,” said Jay Carney, the White House press secretary.

Losukov, responding to messages from a reporter on Twitter, rejected the US assertion that he had been the first to disseminate the recording.

“Disseminating started earlier,” he wrote, adding that his post was being “used to hang the blame” on Russia.

The secret tape, reported Thursday by the Kyiv Post, came to light as a Kremlin adviser, Sergei Glazyev, accused the United States of funding and arming protesters in Kiev and seemed to threaten Russian intervention.

Urging Ukrainian authorities to crush what he described as an attempted coup by US-armed “rebels,” Glazyev said in an interview published Thursday in a Ukrainian edition of a Russian newspaper that Washington was violating a 1994 agreement by trying to shape events in Kiev. “What the Americans are getting up to now, unilaterally and crudely interfering in Ukraine’s internal affairs, is a clear breach of that treaty,” said Glazyev, who advises President Vladimir Putin of Russia on Ukraine.

This, he said, gave Russia the legal right to intervene in the crisis.