Ukraine's pro-Western president has said talks with Russian President Vladimir Putin represent a new chapter in relations between the two states.
Mr Putin's visit signals improving ties between Russia and Ukraine
Mr Putin is visiting Ukraine for the first time in nearly two years amid signs of improving ties.
Relations have been strained since the pro-Western Viktor Yushchenko defeated the Kremlin-favoured candidate for the presidency two years ago.
Mr Putin described the talks as both friendly and businesslike.
Speaking after his meeting with Mr Yushchenko, he said that only co-operation between the two countries could guarantee energy security in Europe.
The Russian president's visit comes nearly a year after Russia briefly cut off natural gas supplies to the former Soviet republic over a price dispute.
Last month, Moscow announced that Ukraine - which remains heavily dependent on Russian gas - would have a smaller increase in the price of gas imports than its neighbours.
Mr Yushchenko, said that trust, mutual understanding and political will were needed to tackle many of the disagreements between the two neighbours.
"On many issues there is pure politicisation that stands in the way of removing them from the agenda," he said.
But he said the lack of a confrontational attitude in addressing these issues was "the biggest breakthrough of today."
The visit comes amid an escalating power struggle between Ukraine's president and prime minister.
The pro-Russian Prime Minister, Viktor Yanukovych, is increasingly edging out the president.
Since his election, Mr Yanukovych has made it a key part of his policy to improve ties with Moscow, damaged after the 2004 Orange Revolution.
The BBC's Helen Fawkes, in Kiev, says that the trip has been seen by some as an attempt by Russia to boost its influence over Ukraine now that a prime minister seen as friendly towards Russia is in place.
During the meeting, the two presidents also discussed Russia's Black Sea fleet, which is currently based in Ukraine.
The lease for the naval base is due to run out in 10 years' time, and Moscow is keen to extend this.
Mr Putin said the Black Sea fleet was an important factor in regional security and stability, but said that the interests of both countries should be taken into account.