Rice said on NBC's "Meet the Press" that underlying the flaring political strife in Ukraine was a "very, very fragile" national economy that needed rapid reforms.
The Obama administrator planned to work with the International Monetary Fund to provide unspecified financial aid to Ukraine, which is seen at risk of default.
Ukraine's leadership was up in the air Sunday following the ouster of President Viktor Yanukovich, an ally of the Kremlin in neighboring Russia. Yanukovich riled up the Ukrainian people last year by doing an about-face and seeking closer economic ties with Russia rather than seeking a closer relationship with the European Union.
Yanukovich's downfall raised concerns that Russia might intervene militarily in the crisis in order to keep Yanukovich in power. Rice told NBC that would be a "grave mistake" and Ukraine should be allowed to hold elections and work out its own problems.
"It's not in the interest of Ukraine or of Russia or of Europe or of the United States to see a country split," Rice said. "It is in nobody's interests to see violence return and the situation escalate."
Russia has more at stake in Ukraine than keeping an ally in office, she said. NBC said Russia has a major naval base in Sebastapol and supplies Ukraine with much of its oil and natural gas.
Yanukovich and Russian President Vladimir Putin had worked out a $15 billion loan deal that was derailed by the political crisis.
Notable deaths of 2014 [PHOTOS]