The new banking regulator has given Lloyds Banking Group and Royal Bank of Scotland (RBS) the green light to bolster their capital positions without asking shareholders, investors or the taxpayer for more cash.

The state-rescued banks' shares crept up again yesterday as the Prudential Regulation Authority (PRA), part of the Bank of England, said it had specified capital strengthening for Lloyds and RBS and would disclose more information after completing talks with all the UK banks.

Both banks immediately said their business plans were on course to deliver the necessary improvements, without recourse to further external fundraising, though RBS noted it still had the "option" of using contingent instruments.

The developments came as the International Monetary Fund (IMF) told the UK Government that if necessary it should not hesitate to plough more taxpayer funds into the banks, on top of the £65 billion already injected, as it would help the economy.

RBS confirmed it expected to improve further its core Tier 1 capital ratio, by continuing to shrink its markets business and non-core assets, and the partial flotation of its US subsidiary Citizens. At last week's annual meeting, chief executive Stephen Hester said the bank's capital ratios were transformed "but we have another 18 months or so to get them in the final shape we and our regulators want".

Yesterday Mr Hester said: "We are pleased with RBS's progress and momentum towards completing RBS's return to full financial health." He said the core business had "plentiful surplus funding to support continued growth in lending" to the economy.

The Tier 1 ratio at RBS was 8.1% at the end of the first quarter, while Lloyds at its annual meeting last week said its ratio was expected to top 9% by the end of 2013 and be above 10% by the end of 2014. At the ailing Co-operative Bank the ratio was 6.3% at the end of 2012.

Lloyds said it expected to meet new targets through a strongly capital-generative core business, a customer-focused strategy, and further non-core asset disposals, adding: "These additional capital requirements are expected to be met without recourse to further equity issuance or the utilisation of additional contingent capital securities."

António Horta-Osório, chief executive, said: "Our strong capital position enables the group to actively support growth and lending in the UK economy as well as delivering sustainable results for our shareholders."

The Washington-based IMF said: "Any strategy should seek to return the banks to private hands in a way that maximises the value for taxpayers, strengthens confidence and competition in the sector, and minimises outward spillovers. In this context, if a sovereign backstop is required to meet a capital shortfall, it should be provided, as this would have a high multiplier." The IMF said a sell-off strategy should be outlined by the end of the year.

The Bank of England's Financial Policy Committee disclosed earlier this year that UK banks would have to raise a further £25bn to absorb future shocks.

Lloyds shares were up nearly 2% yesterday and are now firmly above 61p, the level at which the bank will consider paying out a bonus to Mr Horta-Osório if one-third of the stake is sold off above this price. RBS shares were up 6p at 348p, still well off the 407p to 502p required for the taxpayer to get his money back.

l Lloyds made an immediate move to accelerate its disposal of non-core assets yesterday when it announced the sale of a 15% stake in wealth manager St James's Place, raising £500 million. Lloyds sold a 20% stake in March and agreed a 12-month lock-in, which advisers Merrill Lynch have waived on condition of a six-month lock-in on the bank's remaining 21% stake.