FRANKFURT, March 28 (Reuters) - Germany would need three years to organise alternative gas supplies to become independent of gas from Russia, the chief executive of utility E.ON said on Monday, as Germany pushes back against demands by Moscow to be paid in roubles for its gas.

"We would estimate that it would require a period of three years," E.ON CEO Leonhard Birnbaum told German TV news programme Tagesthemen on Monday, when asked how fast Germany could wean itself off Russian gas.

Without Russian gas supplies the German economy would suffer "massive damages, which should be avoided if in any way possible," he added.

Germany's gas network regulator will prioritize use for heating in residential housing over industrial use, which would cause energy hungry manufacturers such as steelmakers to bear the initial brunt of any supply cuts, said Birnbaum.

He also warned of second-round effects due to shortages of components and intermediate goods in various downstream industries.

At a meeting of European Union leaders on Friday, no common position emerged on Russia's demand last week that "unfriendly" countries must pay in roubles, not euros, for its gas. This was in the wake of the United States and European allies teaming up on a series of sanctions aimed at Russia for its invasion of Ukraine.

(Reporting by Ludwig Burger and Scot Stevenson; editing by Richard Pullin)