The call comes as the TUC outlines demands for a major shake-up of the UK banking sector ahead of its annual conference in Brighton.
Proposals include a crackdown on irresponsible risk-taking by forcing banks to pay corporation tax on bonuses.
The Edinburgh-based Green Investment Bank should also have real borrowing powers so it has the teeth to tackle climate change, according to the TUC.
Brendan Barber, the General Secretary of the TUC, accused the Tory-LibDem Coalition of not doing enough to clean up the sector and ensure it helps the economy.
"Banks caused the crash. Their problems are still driving the eurozone crisis. They are still failing to provide the finance that Britain's productive sectors need," he said.
"Yet the Government is still tiptoeing round reform."
There have been growing calls for ministers to nationalise RBS in recent months.
Earlier this year it was reported that the Cabinet discussed the move as a possible way to tackle a chronic lack of funding to small businesses.
The UK Government would have to spend an estimated £5 billion to buy the share of RBS it does not already own.
But ministers would be open to accusations they were throwing good money after bad, with taxpayers still no closer to recouping the £45 billion used to bail out the bank at the height of the 2008 banking crisis.
The Coalition Government still has a more than 80% stake in RBS, making the bank effectively state-owned.
Ministers are currently struggling to pull the UK economy out of its second recession in five years.
Small businesses have consistently complained they find it difficult to access finance to allow them to grow and expand.
Even if loans are available, they are often at exorbitant rates of interest, business leaders warn. At the same time, the Coalition has identified growth in the small business sector as one of its key economic aims.
According to the latest proposals, nationalising the bank could change its remit from "maximising short-term shareholder value ... to supporting long-term growth" and helping finance UK companies.
It is part of a raft of demands the TUC General Council will put to its conference next week.
These include making company directors legally responsible for their firms' long-term interests. Workers should also sit on committees that decide executive pay and bonuses, the TUC argues, while any payment in excess of £250,000 should be subject to corporation tax.
The proposals also call for increased competition in the banking sector – so that in future fewer banks are considered "too big to fail".
The TUC also reiterated calls for a financial transactions "Robin Hood" tax and for the introduction of regional small business banks.
Meanwhile, the Tories have called on Ed Miliband to stop taking cash from one of the UK's largest unions until its calls off a strike threat.
Len McCluskey, the leader of Unite, has said he expects a new wave of industrial action over pay and conditions.
"There is a real chance of co-ordinated action, if not this winter then certainly early next year", Mr McCluskey said.
Conservative party chairman Grant Shapps said: "Labour's single biggest union paymaster is threatening British businesses with mass strikes as his trade union continues its takeover of the Labour Party. Ed Miliband must refuse to take a single penny more of this union baron's cash until Len McCluskey withdraws his irresponsible threat to sabotage our economy."
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