Rob MacGregor, from the trade union Unite, said the union was "appalled that thousands of people, who form the backbone of the RBS operations, are to be made redundant".
"These employees are totally blameless for the current position which RBS is in, yet they are paying for the mistakes at the top of the bank," he said.
The cuts come on top of the 2,700 job losses already announced by RBS in Britain this year.
Stephen Hester, the bank's chief executive, defended the job cuts, saying it was part of a strategy to "restore the bank to standalone strength as soon as practicable".
"From this we want the government to be able to realise value from its investment in RBS. To do so we need to cut our costs, as in all businesses, given the current recession."
Earlier, RBS confirmed that the government had raised its stake in the group to 70.3 per cent, after investors snubbed a sale of new shares, launched last month, that was backed by the government.
The bank, ravaged by the credit crunch and its 2007 takeover of Dutch group ABN Amro, said in a statement that investors bought just 0.7 per cent of new shares, which left the government to pick up the tab.
The state acquired a 57.9 per cent stake earlier this year after RBS took $28.7bn of government funds.
The government's stake could climb even higher after RBS agreed earlier this year to ring-fence $479bn of assets into the British government's insurance scheme for toxic assets.
The state bailout of RBS, which posted the biggest loss in British corporate history in 2008, has sparked fury in Britain, with ire particularly reserved for Fred Goodwin, the former head of RBS who has received a substantial pay-off, despite presiding over the bank's struggles.
Goodwin has refused repeated government requests to voluntarily give up part of his £700,000 ($1m) pension.
Anti-capitalism protesters who staged a demonstration in central London on the eve of last week's G20 summit in London broke into an RBS office and attempted to steal office equipment before being forced out by police.