Deputy First Minister John Swinney has demanded answers from banking bosses as it emerged three branches have been selected for closure in Perthshire.
TSB is to cut around 300 jobs in Scotland and close 73 branches north of the border next year as part of wider cuts across the high street bank.
Among the TSB branches to close are Blairgowrie, Coupar Angus and Pitlochry.
Other bank workers in Tayside and Fife will be informed today whether their branch is planned for closure.
A “significant change in customer behaviour” has driven the decision, the bank said, with more people also adopting digital banking.
Perthshire North MSP John Swinney said the move would mean there would be no bank in Coupar Angus,
He said: “This is very concerning news both for the affected communities and the local branch staff.
“Should these closures proceed, it will mean that Coupar Angus will now have no bank branches of any kind within the town.
“Accordingly, it is important that steps are taken to ensure my constituents have access to banking services.
“I have spoken to TSB management this morning in order to get a clearer rationale for their decision and to discuss ways to mitigate the negative impact these closures will have on local communities.
“I specifically brought up the idea of mobile banking, and I would be happy to assist TSB in exploring this option in the months ahead.”
TSB operates four branches in Dundee as well as Broughty Ferry’s Brook Street.
It has four branches in Angus – in Arbroath, Carnousite, Montrose and Forfar.
The bank operates from Perth Aberfeldy and Crieff.
TSB also has sites in Rosyth, Dunfermline, Cowdenbeath, Cupar, Burntisland, Glenrothes, Buckhaven, Leven, St Andrews, Anstruther and two sites in Kirkcaldy.
The Edinburgh-based company said the branches earmarked for closure in 2021 have been selected to ensure 94% of customers in Scotland are still within 20 minutes’ travel time of one that will remain open.
It said it will continue to invest in its 62 remaining Scottish branches over the next two years “to radically improve the customer experience”.
As part of that investment, 50 mobile advisers will be introduced in some rural communities to help existing customers and organise further support.
Robin Bulloch, TSB customer banking director, said: “These decisions are the most difficult we take, but we must always be guided by our customers – and we are clearly witnessing a substantial shift towards digital banking.
“We operate a more extensive branch network than most other banks in Scotland, including some much larger than TSB, and we need to reduce its size to reflect the changing needs of our customers and a fast-evolving operational environment.
“TSB remains committed to offering high-quality banking services in branches across Scotland.
“We are also introducing mobile advisers to ensure we look after vulnerable customers and those in rural locations.
“We are working to ensure the transition towards digital – which is being seen right across the economy – is handled sensitively and pragmatically for our colleagues and customers.”
Across the UK, the Spanish-owned bank will cut around 900 jobs and close 164 branches.
It will leave TSB with 290 branches, more than halving its store estate over the past seven years.
Perth and North Perthshire MP Pete Wishart said: “This is really disappointing news for Blairgowrie, Coupar Angus and Pitlochry.
“Over the past few years we have seen a succession of branch closures across Perthshire, and it has had a significantly negative impact on the local communities.
“I’m also concerned about where these proposed closures will leave some vulnerable customers, particularly older people who are most comfortable banking in person.”