LONDON, Feb 21 (Reuters) - Rupert Murdoch's Sun on Sunday newspaper said Prime Minister David Cameron had failed to get a proper deal for Britain from other European Union leaders and was now on the wrong side of history by supporting membership.

The open opposition of Britain's most popular newspaper is a blow for Cameron who has said he will fight for membership in a referendum he has called for June 23.

"Whatever we think of David Cameron's deal and the case for remaining in the EU, we don't doubt his sincerity. We just think he's wrong," the Sun on Sunday said in an editorial.

"His failure to get a worthwhile deal means that he's now on the wrong side of history," the newspaper said in an edition which also ran an article by Cameron arguing for membership.

Cameron said that Sun on Sunday readers would be "key voters in one of the biggest decisions of our lifetimes".

Murdoch opened up the possibility that some of his newspapers could oppose membership on Saturday when he congratulated one of Cameron's closest political allies, Justice Secretary Michael Gove, for opposing Cameron on the EU.

"If we vote to stay after making such a fuss about leaving, the rest of the EU will conclude that although we moan a lot, when push comes to shove we've not got the fight to actually do anything," the newspaper said.

"Yes, the Leave campaign may be chaotic, with petty arguments between the different groups ... But that doesn't mean the fundamental argument is wrong." (Reporting by Guy Faulconbridge; Editing by William James and Alison Williams)