By Max Colchester and Ian Walker 

LONDON--The U.K. government on Tuesday said it had sold a 5.4% stake in Royal Bank of Scotland Group PLC, raising GBP2.08 billion ($3.24 billion) and kicking off a long-awaited privatization of the lender.

UK Financial Investments Ltd., the body that manages the government's bank shareholdings, said it had sold the shares at 330 pence each, representing a 2.25% discount to the bank's closing share price on Monday.

The issue was 2.4 times oversubscribed, with the majority of buyers being short-term investors, according to a person familiar with the matter. The U.K. said Monday it planned to start selling its stake in RBS via an overnight book build.

Shares in RBS fell 0.8% in early trading in London.

Following the sale, the U.K. Treasury's economic interest in RBS, which includes its holding of ordinary shares and B shares in the company, will be reduced to 72.9%. It has agreed not to sell any more shares for 90 days.

RBS Chief Executive Ross McEwan welcomed the sale of the shares, which the government acquired when it bailed out the bank in 2008.

"It's an important moment and reflects the progress we are making to become a stronger, simpler and fairer bank. There is more work to be done but we're determined to build a bank the country can be proud of," Mr. McEwan said.

The U.K. government pumped in GBP45.5 billion to rescue RBS during the financial crisis at an average price of GBP5 a share, meaning the British taxpayer will lose money from the share sale.

U.K. Chancellor George Osborne said the sale was the right think to do for the British economy.

"I wasn't the Chancellor who bailed out RBS; but I am the Chancellor now responsible for doing the right thing for the British economy," Mr. Osborne said. "So while the easiest thing to do would be to duck the difficult decisions and leave RBS in state hands; the right thing to do for the economy and for taxpayers is to start selling off our stake."

Write to Max Colchester at max.colchester@wsj.com and Ian Walker at ian.walker@wsj.com

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