Speaking to reporters on April 18 as she received Estonian President Toomas Hendrik Ilves in Washington, Rice also said Washington remains "absolutely committed" to Georgia's territorial integrity.
Later in the day, State Department spokesman Sean McCormack said Washington urged Russia "to live up to its statements of support for the principles of Georgian sovereignty and territorial integrity and to repeal the April 16 instructions."
Russian President Vladimir Putin on April 16 ordered his government to recognize some documents issued by separatist authorities in Abkhazia and South Ossetia, and to tighten links with businesses and organizations registered in the two pro-Moscow provinces.
The United States, NATO, and the European Union have all called on Putin to reverse the order calling for the establishment of legal links between Russia and the two breakaway regions.
In an apparent attempt to ease tensions, Russian Foreign Ministry spokesman Mikhail Kamynin on April 18 announced steps toward normalizing relations with Georgia and lifting economic sanctions.
But McCormack said Russia's announcement "does not affect or speak" to the April 16 instructions.
McCormack noted that Moscow had already unilaterally annulled economic and military sanctions against Abkhazia, saying this "has raised concerns over military transparency in the region" and "undermines the peace process."
In a telephone interview to RFE/RL's Georgian Service, Georgian Deputy Prime Minister Giorgi Baramidze criticized Russia's move.
"It is not only very dangerous but also a provocative step, aimed at destabilizing the situation in our country and the whole region," Baramidze said. "Georgia is not interested in any kind of military confrontation with anyone, especially on its own soil. Georgia needs peace. Therefore, we are not talking about military confrontation or military plans. We are talking about diplomatic, legal, and political steps we are going to undertake."
Baramidze was speaking on April 18 from Brussels, where he met with NATO Secretary-General Jaap de Hoop Scheffer and EU External Relations Commissioner Benita Ferrero-Waldner.
At a news conference, Baramidze urged the international community not to let Russia legalize the de facto annexation of Abkhazia and South Ossetia.
He said Europe and the Euro-Atlantic community "must react" to prove they are willing to "protect young democracies."
Baramidze said it was "clear" that Russia's move to forge closer links with the two separatist regions was related to Kosovo's declaration of independence and NATO's expansion.
President Putin’s order came after Georgia secured a pledge of eventual NATO membership during the alliance's Bucharest summit earlier this month. It also followed the recognition by many Western nations of Kosovo's February declaration of independence from Serbia, which Moscow opposes.
But McCormack insisted that Kosovo "is and was a unique situation and does not serve as a precedent for any other situation."
Tbilisi has asked for an emergency UN Security Council meeting, which council President Dumisani Kumalo said is likely to be held early next week.