Scottish Labour leader Richard Leonard has called on MSPs to back a campaign to stop RBS from closing more than a third of its branches.
He lodged a motion for debate in the Scottish Parliament, urging members to get behind calls for the UK Government to intervene.
RBS announced plans to close 62 branches in Scotland with the loss of 158 jobs, in a move driven by the fact more people are choosing to bank online or on mobile phones.
The state-backed lender also plans to close 197 NatWest branches in England and Wales by mid-2018.
Trade union Unite described the decision as “morally bankrupt”.
Mr Leonard said the closures went against the bank’s 2010 promise not to shut branches if they were the last bank in town.
He said: “This announcement by the Royal Bank of Scotland will damage high streets the length and breadth of Scotland.
“It will lead to the direct loss of more than a hundred of jobs – and the indirect loss of many more.
“It will hurt the elderly and the vulnerable, who depend on local banks the most.
“The people of the UK own a majority of RBS and – if RBS bosses won’t listen to reason – the UK Government must intervene to stop these closures.”
Unite has called on the Scottish Government to act to convince the bank to change course.
Business minister Paul Wheelhouse said legal and regulatory powers over banking are reserved but he is seeking a meeting with RBS and the UK Government as “a matter or urgency”.
The Treasury has said branch closures were commercial decisions in which it did not intervene.
A spokeswoman for RBS said the majority of branches closing in Scotland (72%) would have either a community banker or mobile branch stop available.
She said: “We have listened closely to feedback from local communities and have extended the time between announcing our decision and the branch closure to six months.
“This has been done in order to ensure our customers have time to consider the right banking options for them.
“Customers will also have a range of alternative ways to bank, including online and mobile for simple transactions, telephony and webchat for assisted help, and the Post Office for face-to-face interactions.”