Britain's government has begun selling its majority stake in bailed-out Royal Bank of Scotland (RBS) to reduce state debt and kick-start the lender's full return to the private sector, the Treasury said Tuesday.

The government has sold 5.4 percent of RBS for £2.1 billion ($3.3 billion, 3.0 billion euros), a statement said.

Royal Bank of Scotland was rescued with £45.5 billion of public money in 2008 at the height of the global financial crisis.

The world's biggest bank bailout handed Britain's government with about 80 percent of the Edinburgh-based lender.

RBS has since reported losses totalling about £50 billion and has axed more than 30,000 jobs, with thousands more reportedly set to follow.

"The government has today begun the process of selling its shares in the Royal Bank of Scotland. It has sold 5.4 percent of the bank at a price of 330p per share," the Treasury said Tuesday.

"The £2.1 billion raised from the sale will be used to pay down the national debt."

But with the state having bailed out RBS at a cost of 500 pence a share, the taxpayer is taking a sizeable hit on the sale.

Finance minister George Osborne insisted that the move was "an important first step in returning the bank to private ownership, which is the right thing to do for the taxpayer and for British businesses".

He said the move would "promote financial stability, lead to a more competitive banking sector, and support the interests of the wider economy."

Back in February, Royal Bank of Scotland said it would end investment banking in the Middle East and Africa and significantly reduce its presence in Asia and the US after a seventh straight annual loss for 2014.

But it recorded a 27-percent rise in net profits for the second quarter of this year, with the sale of US operations offsetting higher exceptional costs.