Kirkilas made the comment to Slovenian Prime Minister Janez Jansa in a telephone conversation on Wednesday, according to Lithuanian government's information bureau.
Slovenia currently holds the EU's rotating presidency and will preside over the March 13 and 14 summit of the bloc's heads of state and government in Brussels.
Kirkilas's request comes as Lithuania is facing the closure in 2010 of a Soviet-era nuclear reactor which currently satisfies 70 percent of the energy needs of the small ex-Soviet Batlic republic.
The move will leave it almost completely dependent on gas supplies from Russia, a partner which has been known to cut natural gas deliveries to neighbouring countries -- most recently Ukraine.
Lithuania vowed to shut down the Chernobyl-type reactor as part of its EU membership agreement. A new Ignalina nuclear facility is planned, but will be ready by 2015 at the earliest.
Politicians and non-government organizations are already mulling plans to keep Ignalina going.
Lithuania's Chief Election Commission on Monday registered an initiative group aiming to collect 300,000 signatures supporting the referendum to extend Ignalina's operations.
Some politicians also support the idea and plan to initiate the referendum in the parliament.
But an extension of the plant's life is highly unlikely under strict EU regulations.