The newly elected president of Ukraine, Viktor Yanukovych has suggested he would allow Russia's Black Sea Fleet to remain in his country beyond 2017.
Mr Yanukovych, during his first visit to Moscow since his election last month, said he would open a "new page" in relations with Russia.
Russian President Dmitry Medvedev said he hoped the "black streak" in ties between the two nations would be over.
Tensions rose under Ukraine's previous Pro-Western administration.
Mr Yanukovych's predecessor, Viktor Yushchenko, had wanted Ukraine to join Nato - a move strongly opposed by Moscow.
After talks on Friday with the new Ukrainian president, Mr Medvedev said there could now be full co-operation at all levels.
Mr Yanukovych responded by saying that all major issues which had been causing tensions could now be dealt with.
On the Black Sea Fleet, he said the issue would be resolved soon in a way "that will satisfy both Russia and Ukraine".
The fleet is stationed in the port of Sevastopol in southern Ukraine, but its lease runs out in 2017 and its fate has long been a contentious issue between Moscow and Kiev.
The Kremlin is keen to extend the lease. Mr Yushchenko had opposed the move, but Mr Yanukovych has promised to seek a compromise.
Mr Yanukovych defeated pro-Western candidate Yulia Tymoshenko, in February' s presidential election.
Moscow is delighted that the pro-Western leaders of the Orange Revolution have now been defeated, the BBC's Richard Galpin reports from the Russian capital.
The big question is how far the reconciliation between Moscow and Kiev will go, our correspondent adds.
Gas supplies may be a source of friction in the talks.
Officials say the Ukrainian leader is expected to lobby for lower gas prices, as well as seek billions in loans from Russia to help cover the country's soaring budget deficit.