Germany's Uniper, RWE have paid for Russian gas under new scheme

* First payments under new rules were due end-May

* Moscow has drawn up new payment protocol to pay for gas

* Gazprom has cut supplies to Dutch GasTerra

FRANKFURT, May 31 (Reuters) - German companies Uniper and RWE have paid for Russian gas under a new scheme proposed by Moscow, in a bid to ensure continued supply of the fuel that is critical to Europe's top economy.

Russia's payment scheme, which involves setting up accounts that would be paid in euros and then swapped for roubles, has exposed cracks in Europe's united response towards Russia for its February invasion of Ukraine, with some countries refusing to pay and others finding ways to comply.

Germany greatly depends on Russian gas, which accounted for more than half of all imports of the fuel last year. Uniper and RWE, two major German importers of Russian gas, have said they would establish accounts in Russia in line with current sanction laws to make sure gas flows continue.

"Like other German and European companies, Uniper has changed the payment method for gas deliveries from Russia. Uniper pays in euros in accordance with the new payment mechanism," Uniper said in e-mailed comments.

"The first of these payments was made at the end of May. Uniper is therefore acting in compliance with sanctions and can continue to ensure timely fulfillment of the contract."

A spokesperson for RWE, too, confirmed that euros had been transferred to the Russian account that was set up to enable payments.

Russia's Gazprom earlier on Tuesday said it has fully cut off gas supplies to Dutch gas trader GasTerra after it had failed to make payments for gas delivered in April, making good on its promise to shut down deliveries over payment issues.

Uniper last month said that the first payment under the new guidelines would be due at the end of May, leaving open the exact date.

Uniper said the process has been coordinated with the German government and follows the EU guidelines. (Reporting by Christoph Steitz, Tom Kaeckenhoff, Vera Eckert and Madeline Chambers; Editing by Jon Boyle and Grant McCool)