Ukraine, which depends heavily on gas imports from Russia, has long wanted to revise a 2009 gas deal with Moscow which it argues set an exorbitant price for the fuel (see background).
But President Viktor Yanukovich's talks with Putin, just like those with the Kremlin leader's predecessor - and now prime minister - Dmitry Medvedev, failed to yield a breakthrough.
"There are issues where we have not reached an agreement but ... we will aspire to do that," Putin told reporters when asked about the gas issue after talks in the Black Sea resort of Yalta.
In order to get a discount, Moscow insists that Ukraine must either let Russian energy giant Gazprom take over its gas pipelines - which carry Russian gas to Europe - or join a Russia-led Customs Union, a post-Soviet trade bloc.
Kyiv sees its gas pipelines as a strategic asset and has long sought a free trade deal with the European Union. It has so far refused both trade-offs.
However, the high price of gas is a heavy burden on the state budget and the economy, and is one of the main headaches for Yanukovich's government as it prepares for a parliamentary election in October.
On Thursday, Yanukovich said Ukraine was still looking at the Moscow-led customs union.
"We are not saying 'No', we are thoroughly and seriously studying these integration processes," he said.
Ukraine's free trade deal with the EU, already agreed in principle, was shelved after the imprisonment of Yanukovich's key political opponent, former Prime Minister Yulia Tymoshenko, last October in a trial which Brussels saw as politically motivated.
A Ukrainian court found Tymoshenko guilty of overstepping her powers as prime minister while forcing through the same 2009 gas deal with Russia which Yanukovich is now trying to renegotiate.
