Arseniy Yatsenyuk said Kiev could solve the crisis quickly if Moscow stopped meddling in the situation.
Russian Foreign Minister Sergei Lavrov warned that Kiev’s policies were pushing Ukraine into “fratricidal war”.
Earlier this week rebels and government forces were embroiled in some of the worst fighting of the crisis so far.
The separatists say they lost up to 100 fighters as they tried to seize Donetsk airport from pro-Kiev forces.
Ukraine’s interior ministry says the military is now in full control of the airport, although gunfire was reported in Donetsk itself on Wednesday.
Speaking on a visit to Germany, Arseniy Yatsenyuk said the situation in the east was deteriorating and Russia’s involvement was causing huge difficulties.
“A number of trucks full of live ammunition, full of Russian-trained guerrillas crossed the Russian border into Ukraine,” he said.
“We ask Russia and Putin to block the border to Ukraine. If Russia is out of this game we can handle this situation in a week.”
Meanwhile, the Organization for Security and Co-operation in Europe (OSCE) said it had re-established contact with a monitoring team it reported lost in eastern Ukraine on Tuesday, but it continued to refer to the group as “detained” and their fate is unclear.
UN Secretary General Ban Ki-moon has called newly elected President Petro Poroshenko to congratulate him on receiving a “strong mandate” to govern.
Moscow had criticized the election because many in the east were unable to vote as a result of the unrest.
But analysts say the election has bolstered the confidence of Ukrainian officials in their dealings with Moscow.
On Tuesday, Arseniy Yatsenyuk denied Moscow’s long-standing claim that Ukraine owed billions of dollars in unpaid gas revenues.
The prime minister said that in fact Russia’s state-owed Gazprom owed Ukraine $1 billion in compensation for natural gas seized in the annexation of Crimea.
Gazprom’s chief executive Alexei Miller said on Wednesday that Ukraine had used $1.7 billion worth of gas in May alone, and would owe $5.2 billion by June 7.
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