Speaking to The Associated Press, Prime Minister Arseniy Yatsenyuk denied reports that Ukraine is seeking military assistance from the United States.
Since last weekend, Russian troops have taken control of much of the Crimea, a peninsula in the Black Sea where Russian speakers are in the majority.
Yatsenyuk, who took office last week, blamed Russian President Vladimir Putin for causing one of the sharpest international crises in Europe since the end of the Cold War - and expressed fears about further possible Russian incursions.
Asked by AP if he was afraid that Russia might send troops to occupy other Russian-speaking areas of Ukraine, Yatsenyuk said: "Let me put it bluntly: yes, it's still a concern and Russia is to realize its responsibility and Russia is to stick to its international obligation, to stop the invasion.
"Mr. President (Putin), stop this mess," said Yatsenyuk.
The prime minister, approved by parliament on Feb. 27, also denied a report that cash-strapped Ukraine was negotiating with the United States for deployment of U.S. missile defenses in exchange for financial help.
"This is not true," Yatsenyuk told the AP. "We have no talks with the government of the United States of America on any kind of deployment of any military forces. The only negotiations we have is to get financial support, financial aid from the United States government in order to stabilize the economic situation in my country. It's absurd."
On Tuesday, Putin said Ukraine's current leaders had come to power as the result of an unconstitutional coup. In the interview, Yatsenyuk blamed Russia's leader for the ongoing crisis and said Putin was the one acting outside the law.
"A number of military forces of the Russian Federation are deployed in Crimea. We cannot figure out the reason why Russian boots are on Ukrainian ground. And it's crystal clear that it was ordered personally by President Putin. This is Ukrainian territory and Russia wants to grab control over Crimea. But I will underline again, we will do our best in order to regain control over Ukrainian territory. The Russian military is to be back in the barracks."
"What happened in Crimea is unconstitutional and resembles ... a coup supported by the Russian government and the Russian military," Yatsenyuk said.
"The Ukrainian government is legitimate. And let me remind Mr. Putin that this government was supported by the constitutional majority of Ukrainian MPs with 371 votes. We are legitimate and we must fulfill our responsibilities. And we strongly recommend to our Russian partners to build up relations with the new Ukrainian government."
A spokeswoman said it was the prime minister's first sit-down interview since he assumed the post. Yatsenyuk, who spoke in English, said he hadn't talked personally to Putin, "but it's in the interests of our countries to start a dialogue."
"First we need to stop the invasion and afterward we want Russia to (be) our partners, real partners and to stop this zero-sum game. It is to be a win-win game where both Ukrainian and Russian interests are considered," he said. "So we urge the Russian government to start real talks with the new Ukrainian government and we ask Russia not to be a neighbor but to become a real partner."
Yatsenyuk, 39, is a millionaire banker who has served as the economy minister, foreign minister, and then parliament speaker. He unsuccessfully ran for president in 2010. He is viewed as a technocratic reformer and enjoys the support of the United States.
Yatsenyuk said Crimea must remain part of Ukraine, but may be granted more local powers. He said was in favor of establishing a special task force "to consider what kind of additional autonomy the Crimean Republic could get."
On Tuesday, U.S. Secretary of State John Kerry visited Kiev to announce $1 billion in U.S. assistance to Ukraine in the form of energy subsides. Yatsenyuk told AP the economy of this former Soviet republic "is in a big mess" - but that the new government is taking action to improve things.
"The state treasury is empty. And due to unbelievable and unlimited corruption in my country we cannot collect revenues in order to execute our social obligations, but despite this we have a clear-cut action plan how to tackle economic problems.
"We resumed talks with the International Monetary Fund. The IMF mission is on the ground. A good gesture made by the United States government to support the state of Ukraine with $1 billion of guarantees is a first sign that Ukraine could be back on track in terms of economic stability.
"But we need to move further."