Yatsenyuk said the world has "reason to be concerned" about Putin's intentions, and Russia undermined global stability by annexing Crimea.
"President Putin has a dream to restore the Soviet Union, and every day he goes further and further, and God knows where is the final destination," Yatsenyuk said. He cited a 2005 speech by Putin to the Russian Federal Assembly in which Putin said the collapse of the Soviet Union was "a major geopolitical disaster of the century."
Also Sunday, Geoffrey Pyatt, the U.S. ambassador to Ukraine, said that a pact reached this past week to de-escalate the crisis in Ukraine is the "best chance that we've got" to do so diplomatically.
Pyatt reiterated the U.S. and European Union view that there is not a military solution to the crisis and that it must be solved diplomatically.
"We’re convinced his is the best chance that we’ve got to achieve a diplomatic de-escalation of this crisis, and we’re working hard at it," Pyatt said from Kiev on CNN's "State of the Union."
Militants in at least a dozen cities in the east of the country have occupied buildings and seized weapons and armored vehicles. Pyatt said he believes that "Russia has influence over some of these groups" and hopes the country exercises that authority to try to implement the framework reached in Geneva.
On Sunday, an Easter truce was shattered by a gunfight that left at least one person dead and three wounded at a checkpoint occupied by a pro-Russian militia in eastern Ukraine. Russia said the clash was evidence that Ukraine was violating the accord reached in Geneva.
The pact calls for all parties to stop violent acts and for the disarmament of illegal groups. The United States says about 40,000 Russian troops are currently on the Russian-Ukrainian border. NATO is also increasing its military presence on its eastern border. Poland's defense minister, Tomasz Siemoniak, told The Washington Post that it expects U.S. ground troops to be dispatched to his country.
“There is an apparent effort from outside to try to stir division, but I’m convinced that those who are trying to stimulate separatism, who are trying to preach violence, are not going to find resonance,” Pyatt said.
Russian President Vladimir Putin said earlier this week that the crisis is putting Ukraine on the brink of civil war.
Pyatt disputed this, saying that most Ukrainians "across the board" have a "desire to bring everyone together." Pyatt said there are "obviously efforts from small isolated groups to stir division," and characterized them as only "about a couple hundred of people." Pyatt said they do not represent the whole of the country. "That's not what I hear from most Ukrainians," he said.
Pyatt said the United States and the E.U. want to see a politically stable Ukraine, and there "is no better answer to Russia" than Ukrainians voting in elections May 25.
Pyatt said there are reasons for unhappiness in the country, particularly economic problems in the eastern part of the country.
Ukraine's military is woefully underarmed and without modern equipment and training, but Pyatt said the United States is not providing Ukraine armament, only support and non-lethal aid.
"Ukraine is outgunned,"he said. "But our efforts have been focused on diplomacy, focused on economic support."
Also appearing on "Meet the Press," Rep. Chris Murphy (D-Conn.) said the U.S. has given Ukraine $10 million in military and financial aid. Congress last month overwhelmingly approved a $1 billion aid package for Ukraine.
Yatsenyuk said that the country has asked for financial support but that it has to modernize its military.
“We need financial, economic support," Yatsenyuk said. "We need to modernize the Ukrainian military and to overhaul all structures of Ukrainian defense systems.”
Also appearing on "Meet the Press," Sen. Bob Corker (R-Tenn.) said that eastern Ukraine will be lost unless the U.S. shifts its strategy. Corker is the ranking Republican on the Senate Foreign Relations Committee.
"I think we're going to lose eastern Ukraine if we continue as we are," he said, "and I think it's going to be a geopolitical disaster if that occurs."
Corker said the U.S. approach to foreign policy is a "day late and a dollar short," and the U.S. needs to be more forceful in its approach toward Russia and increase sanctions on sectors such as energy and banking. Instead, he said, the administration keeps waiting to see what Russia's next steps are rather than acting.
He said the U.S., by not taking a harder line, is essentially allowing Russia to go into Ukraine.
"I think the administration is basically saying, 'look, don't do anything overt, don't come over the border with 40,000 troops, don't embarrass us in this way, but you can continue to undermine the sovereignty of the Ukrainians," Corker said.
Corker said President Bashar al-Assad of Syria also knew he would not be punished by using chemical weapons.
“The wisest thing that Assad did was really to kill 1,200 people with chemical weapons, because in essence we said, 'Don’t embarrass us any more in that way,'" Corker said, adding that Assad was able to kill 60,000 more people with bombs.
"And I think that's what we're saying with Russia," Corker said. "Don't embarrass us, but you can continue the black ops activity."