U.S. Secretary of State John Kerry has condemned what he called Russia's "act of aggression in Ukraine."
Kerry, on a visit to Kyiv, said diplomacy and respect for sovereignty, not unilateral force, can best resolve the dispute over Ukraine.
He said, "there is nothing strong in what Russia is doing." He said the United States "stands with the people of Ukraine," and would prefer to see tensions with Russia deescalate and managed through structures of international institutions.
Kerry arrived in Kyiv on March 4 to show support for Ukraine's new authorities. His visit comes as the United States and its allies step up pressure on Moscow to withdraw its forces from Crimea or face economic sanctions and diplomatic isolation.
U.S. officials travelling with Kerry announced Washington is preparing a $1 billion aid package for Ukraine.
In a March 4 statement, U.S. President Barack Obama said Russia's incursion into Crimea was not a sign of strength but a sign of "meddling" that would push countries away from Moscow. Obama said Russian President Vladimir Putin's reasons for sending Russian forces into Crimea are not "fooling anyone."
After meeting with Kerry in Kyiv, Ukraine's interim Prime Minister Arseniy Yatsenyuk announced his government has made contact with Russian leaders aimed at resolving the crisis. Yatsenyuk said talks are "for now, proceeding timidly, but the first steps have been made."
Putin Press Conference
Meanwhile, President Vladimir Putin has said that Moscow sees no need to send Russian troops into Ukraine but that he does not exclude such a possibility as a "last resort," amid a continued standoff between Ukrainian troops and pro-Russian forces in Crimea.
Speaking at a news conference at his residence outside Moscow, Putin said: "As to the use of [Russian] armed forces [in Ukraine], there is no such necessity at the moment. Nevertheless, such an option is available."
Asked if Russian troops were involved in operations in Crimea, he said, "No, they did not participate," adding that only "local forces of self-defense" were surrounding Ukrainian military bases in the region.
Putin's statement came after Russia's ambassador to the United Nations, Vitaly Churkin, on March 3 said that Ukraine's ousted President Viktor Yanukovych had formally asked Moscow to deploy Russian troops to reestablish law and order in his country.
WATCH: Armed Men Continue Blocking Crimea's Belbek Airfield
At a press conference in Rostov-on-Don on February 28, however, Yanukovych said that he would not seek military assistance from anyone, saying, "Any military action in this situation is unacceptable."
Putin -- in his first public comments on the Ukraine crisis -- called the change of government in Ukraine unconstitutional and said it amounted to an armed coup.
Putin went on to say that dangerous far-right groups have emerged in Ukraine.
"What is our biggest concern? [The fact that] we are witnessing an orgy of neo-Nazis, nationalists, and anti-Semites in some parts of Ukraine, Kyiv included," Putin said.
The Russian leader said Yanukovych is Ukraine's only legitimate president until a new election is held. But he added that Yanukovych has "no political future" and that Russia sheltered him to save his life.
Putin said he understands the Ukrainian people's need for change but that what he called "illegal actions" can't be encouraged.
Putin said normal relations with Ukraine cannot resume until after new elections. But he warned that Russia would not recognize the results of elections in Ukraine that are held under what he called the "current conditions of terror."
The new leadership in Kyiv has set a presidential election for May 25.
Russia earlier on March 4 ordered some 150,000 troops who had been holding military drills near the Ukrainian border back to their barracks.
Putin said that the exercises had been planned for a long time and had no connection to the situation in Ukraine.
Putin said there are no considerations to annex Crimea and that it is up to the citizens of the region to determine their own future. He said Moscow won't instigate such a movement.
Referring to suggestions by Western leaders of a boycott of a G8 summit scheduled to take place in the Russian Black Sea resort of Sochi, Putin said Russia was ready to host the meeting as planned in June, but he said if Western leaders did not want to come, "they don't need to."
With reporting by AP, AFP Reuters, Interfax, and ITAR-TASS