The SNP's Westminster leader said he has had "productive" talks with RBS bosses over its plans to close scores of bank branches.
Ian Blackford added that his discussions were "moving in a positive direction" and said he was hopeful that a breakthrough could be found.
It comes after the state-owned bank announced proposals to close 62 branches in Scotland, including some in remote and rural communities.
RBS has insisted it is responding to changes in customer behaviour, including a rise in digital banking.
But Mr Blackford said many of the affected branches provided "vital" local services, as he accused the Tory Government of "failing to lift a finger" to save them.
He went on to reveal that he has been "bypassing" the Prime Minister and talking directly to RBS chiefs about the plans, in a bid to ensure community concerns are heard.
The MP for Ross, Skye and Lochaber has repeatedly pressed Theresa May on the closures at Prime Minister's Questions, urging her to make the case to keep the branches open to RBS bosses in person.
He hit out at the Conservative Government, accusing it of failing to act on the issue.
Mr Blackford said: "The Tories are letting Scotland down by failing to lift a finger to save these vital local banks from closure - leaving many communities with the damaging prospect of losing their last bank in town."
But he added: "While the UK Government refuses to take action, the SNP will continue our campaign to save these banks, which are hugely important for local people and businesses.
"That is why I have, for the past few weeks, been bypassing the Prime Minister to talk directly with RBS.
"Our discussions have been productive, and are moving in a positive direction. I am hopeful the concerns of our communities are being heard and that a breakthrough can still be found."