British Prime Minister David Cameron says he wants state-controlled Royal Bank of Scotland to speed up restructuring and has refused to rule out giving the government's share in the bank to the public.

The government owns 82 percent of RBS after pumping in 45 billion pounds of capital when the bank neared collapse in 2008.

Speaking in India during a trip aimed at drumming up trade and investment, Cameron made it clear he was keen to return the bank to private ownership as soon as possible and wanted it to step up its efforts to overhaul itself.

"It was a very badly damaged institution but I think they are doing the right thing but obviously we want them to, where possible, accelerate the adjustments that they are making in terms of making it a strong organisation," he said.

When asked to comment on reports the government was considering giving away its stake by 2015, Cameron said:

"These are all interesting questions for the future. The first job is to turn around the performance of RBS and to strengthen its balance sheet, strengthen its business and that's what (RBS Chief Executive) Stephen Hester and his team are doing.

"But I am keen to examine all possibilities for what we can do to put RBS in time back into the private sector."

In October, RBS said it was preparing to sell the shares in 2014, one year before the next general election, with the timing and sale structure up to the government. No share giveaway was mentioned.

Deputy Prime Minister Nick Clegg in 2011 backed proposals to give the public shares in part-nationalised banks because taxpayer money had been used to keep the banking system alive.

At the time, the Treasury said it would "look at all options", but critics dismissed the idea as a headline-grabbing exercise.