Chancellor of the Exchequer George Osborne also announced plans to reduce the state's stake in privatised postal service Royal Mail.
RBS is about 81% state-owned by the UK taxpayer after being rescued in a £45.5bn bailout following the 2008/9 financial crisis.
Osborne told a City audience at London's Mansion House that the government could get less for RBS than the 500p per share that the taxpayer paid for it.
But he said: "It's the right thing to do for British businesses and British taxpayers. Yes, we may get a lower price than that was paid for it - but we will get the best price possible.
"The longer we wait, the higher the price the whole economy will pay."
The sale is thought to be partly politically motivated as the Tories claim privatising RBS will help it restore its battered fortunes more rapidly. They also believe it will help them to reduce Britain's national debt.
But trade unions attacked the planned sale, saying the government was short-changing the public. RBS shares rose 2.9p to 357.7p in early trading in London.
The placing price was 500p per share, resulting in proceeds of £750mln. Ministers also intend to gift up to 1% of the shares in Royal Mail to the group's UK staff, subject to restrictions on sale, from the government's remaining holding.
But opposition party Labour attacked the move, saying the government should have given individual investors rather than institutions a chance to buy the shares.
Royal Mail shares fell 16.6p to 499.9p in early trading in London.