Ian Blackford clashed with the Prime Minister over the closures, which will see 62 RBS branches disappear in Scotland, many of them from high streets in isolated rural towns and villages.
During Prime Minister’s Questions, Mr Blackford said the government, which still owns a 73% share of the bailed-out bank, should “step in and tell the Royal Bank of Scotland to keep their commitments and not close the last bank in town.”
Mrs May said the Scottish Secretary David Mundell had met with RBS executives to express his concern about the closures, but that decisions about branches were up to individual banks.
She added that banks were required to meet the Acess to Banking Standard to ensure that essential services were still available to customers, and that some banking functions would still be possible in places where branches were closed, through the Post Office.
Mr Blackford dismissed the Prime Minister’s response, saying it was time to “summon Ross McEwan”, the RBS chief executive, and tell him “this is not acceptable”.
Meanwhile, the 12 back bench Scottish Conservative MPs have written to the Treasury to say they were “not reassured” by RBS following meeting with bank executives about the closures.
In a letter to Treasury minister Stephen Barclay, the MPs say measures to maintain services through the Post Office and mobile bank trucks are “insufficient”.
Mr Blackford is due to hold further meetings with RBS on Wednesday.