(Adds Putin’s declaration)

BRATISLAVA, May 15 (Reuters) - Russian President Vladimir Putin has informed multiple European states that gas supplies to Europe through Ukraine may be halted as of June 1 if Kiev does not pay its bills, Slovak Prime Minister Robert Fico said on Thursday.

Fico, speaking to reporters after meeting NATO Secretary General Anders Fogh Rasmussen, said the most pressing threat facing Slovakia was the question of deliveries from Russia that pass through Ukraine.

“Today, multiple member states including Slovakia were informed by President Putin that as of June 1, if Ukraine does not pay for supplied gas, it will not be supplied to the European territory,” Fico said.

“It is a serious threat to the energy security of Slovakia.”

Putin’s declaration, released by the Kremlin on Thursday, said there was a problem with Ukraine’s debt for gas and insufficient levels of storage in Ukraine, and that over the past month there has been no movement on resolving the issue.

“Unfortunately, we have to say that we have not received any specific proposals from our partners as to how to stabilise the situation with the Ukrainian buying company so that it can meet its contractual obligations and ensure reliable transit,” the declaration said.

“Given the circumstances, the Russian company (Gazprom) has issued an advance invoice for gas deliveries to Ukraine, which is completely in accordance with the contract, and after June 1 gas deliveries will be limited to the amount prepaid by the Ukrainian company.”

The dispute does not relate to deliveries to Europe via the Nordstream pipeline but only the one in Ukraine which carries almost half of European supplies from Russia.

Putin also urged European leaders to do more to help Ukraine through its economic crisis and to resolve the standoff over gas.

Moscow has reduced gas supplies to Kiev during two past price disputes, causing disruptions to supplies to Europe as recently as 2009. (Reporting by Jan Lopatka; Writing by Michael Kahn; editing by Jason Neely and Elaine Hardcastle)