MOSCOW (Reuters) - Slovak Prime Minister Robert Fico has rejected a Ukrainian invitation to visit Kyiv this week to discuss gas transit deals, Russia's TASS news agency said on Tuesday, citing a Slovak lawmaker, amid a spat over the end of Russian gas deliveries.

Russia's gas flows to Europe ended at the start of the year after the expiration of a transit agreement between Kyiv and Moscow. Ukraine refused to extend the deal, seeking to stop energy revenue going to Moscow to fund its nearly three-year invasion. Fico says the move has damaged Slovakia's economy.

Ukrainian President Volodymyr Zelenskiy on Monday extended an offer to Fico to visit Kyiv to try and resolve their spat.

The Kyiv visit "is not possible," lawmaker Tibor Gaspar, part of a Slovak delegation currently visiting Moscow, told TASS. "I don't think it will happen," he added, without elaborating.

The Slovak government in Bratislava did not immediately respond to a Reuters request for comment. There was also no immediate comment from Kyiv.

Fico says the end of the transit deal has hurt Slovakia by pushing up gas prices and also terminating transit fees it had earned in sending the Russian gas further into Europe.

He has tried to restore the flows, and travelled to Moscow last month to meet with Russian President Vladimir Putin in the Kremlin, a move which angered Ukraine.

Fico previously said a deal was close that would have seen gas deliveries via Ukraine continue by having it change ownership beforehand. But he claims Zelenskiy rejected extending any gas flows through Ukraine at an EU summit in December.

The Slovak leader has threatened to cut emergency electricity supplies to Ukraine and reduce aid for Ukrainian refugees in Slovakia, among other measures, if the gas transit issue is not resolved.

(Reporting by Reuters; Writing by Lucy Papachristou; Editing by Gareth Jones)