"I think we do agree that all sides should refrain from violence, and that all sides should refrain from any provocation. And we're sending a message to all sides appropriately," Rice said.
Russia's foreign minister said violation of international law resulting from the declaration of Kosovo's independence was unacceptable.
"It's an open secret that the U.S. and Russia's positions [on Kosovo] are opposite," Sergei Lavrov said.
A draft statement on Kosovo proposed by Russia to the UN Security Council last Wednesday was met with skepticism by Western nations.
The statement, which aims to preserve Serbia's territorial integrity and calls for further talks on the Albanian-dominated region's status, was rejected by the countries that have recognized Kosovo's independence - including the United States and Britain - declared on February 17.
Prior to the declaration of independence by the Serbian province, the European Union approved the deployment of a 2,000-strong police and justice mission in Kosovo to replace the UN mission which has been based there since the NATO bombing of Serbia in 1999 ended a conflict between Albanian and Serb forces. Kosovo has been a UN protectorate since the end of this conflict.
Since the predominately Albanian province declared its independence from Serbia, 18 of the 27 EU states have recognized Kosovo. Russia, China, Spain, Cyprus and several other countries have refused to recognize the province's independence.