* Rice calls for rapid changes, elections in Ukraine
* Says situation fluid, Yanukovich's whereabouts unknown
* McCain says Ukraine must not be split, needs assistance (Adds comments from U.S. ambassador to Ukraine, Kerry phone call with Lavrov)
By Will Dunham and Ros Krasny
WASHINGTON, Feb 23 (Reuters) - U.S. officials insisted on Sunday that Ukraine should remain unified and cautioned that any military intervention by Russia would be a mistake after bloody street protests ousted the pro-Moscow president.
In an appearance on the NBC TV program "Meet the Press," National Security Adviser Susan Rice was asked about a scenario in which Russia would send troops to restore a government more friendly to Moscow, or for the country to be carved up.
"That would be a grave mistake. It is not in the interests of Ukraine or of Russia or of Europe or the United States to see the country split. It's in nobody's interest to see violence return and the situation escalate," Rice said.
Rice's appearance provided the most extensive White House comments yet on days of drama in Ukraine in which opposition groups with leanings toward western Europe took control and Russian-backed President Viktor Yanukovich left the capital, Kiev.
Many in Washington regard the next few days as crucial to the fast-unfolding crisis. With the Winter Olympic Games ending in Sochi, Russia, President Vladimir Putin could focus more closely on the Ukrainian situation.
U.S. Secretary of State John Kerry spoke by telephone on Sunday with Russian Foreign Minister Sergei Lavrov, expressing support for the Ukrainian parliament's latest moves. Kerry has also been in touch with some of Ukraine's opposition leaders.
The State Department said on Saturday it would send its No. 2 official, Bill Burns, to Kiev this week.
Rice said the United States wants a reduction of the violence in Ukraine, constitutional changes, democratic elections "in very short order," and the opportunity for Ukrainians to come together in a coalition government.
The fluidity of Ukraine's situation is such that U.S. authorities are not sure where Yanukovich is. There had been reports he has retreated to the pro-Russian eastern part of Ukraine.
"He is in a place where it will reveal itself. Yesterday we knew where he was. Today we're not so sure," Rice said.
The crisis in Ukraine reflects the conflict between those who want the country to remain aligned with Russia and those who want closer integration with western Europe.
But Rice said those goals were not "mutually exclusive".
"There is not an inherent contradiction ... between a Ukraine that has longstanding historic and cultural ties to Russia and a modern Ukraine that wants to integrate more closely with Europe," Rice said.
Ukraine's messy drive toward democracy, during which dozens have been killed, was ultimately positive, Rice said: "Over time, this trajectory is a good one."
Her comments were echoed by Geoffrey Pyatt, the U.S. ambassador to Ukraine, in an interview on Sunday with National Public Radio.
"It's been thrilling, exhausting, but also inspiring," Pyatt said. "What comes in the weeks ahead is a second chance for Ukrainian democracy, a chance to make the institutions work."
On Sunday, Ukraine's parliament, exercising power since mass protests caused Yanukovich to flee, named its new speaker, Oleksander Turchinov, as acting head of state and worked to form a new government.
Pyatt said the United States had been "encouraged" by actions in the Rada, Ukraine's parliament and the "democratic process through which Mr Turchinov was selected as the speaker."
"There are now intensive consultations going on among all the political parties to shape a successor government," Pyatt said.
He said the United States is in close touch with authorities in Ukraine, including the Interior Ministry, the intelligence agency and the police, to urge "the importance of gaining rapid authority over the instruments of state power."
The European Union and Russia, vying for influence over the former Soviet republic of 46 million people on their borders, considered their next moves on Sunday.
Russia, which had provided funding to Yanukovich's government, said it would keep cash on hold until it sees who is in charge.
Asked whether Putin looked at Russia's sphere of influence in Ukraine in a Cold War context, Rice said that "he may".
"But if he does, that's a pretty dated perspective that doesn't reflect where the people of Ukraine are coming from. This is not about the U.S. and Russia," Rice added.
Two lawmakers urged the Obama administration to make clear that Ukraine's territorial integrity must be protected.
"The message has to be sent to him (Putin) that let the Ukrainian people determine their own future, and a partition of Ukraine ... is totally unacceptable," Republican Senator John McCain, a key Republican voice on foreign policy, told the CBS program "Face the Nation".
"And we need to act immediately to give them (Ukrainians) the economic assistance that they need, based on reforms that are going to be required, as well. So it's going to be tough sledding."
Bob Corker, the top Republican on the Senate Foreign Relations Committee, said in a statement: "The United States should do everything possible to ensure Ukraine remains one country and that their territorial and political integrity is maintained, allowing them the freedom to choose a future within Europe."
U.S. Treasury Secretary Jack Lew met his Russian counterpart, Anton Siluanov, on the sidelines of a Group of 20 meeting in Sydney on Sunday to discuss the Ukrainian crisis.
"Secretary Lew emphasized that the United States, working with other countries including Russia, stands ready to assist Ukraine as it implements reforms to restore economic stability and seeks to return to a path of democracy and growth," a Treasury Department official said. (Reporting by Will Dunham and Ros Krasny; Additional reporting by Roberta Rampton in Washington and Ian Chua in Sydney; Editing by Sophie Hares and Grant McCool)