Fine Art Investment and Display, which is registered in the Cayman Islands, says that the Government is bending the rules to help keep the pounds 7.6m sculpture in Britain. It will seek a judicial review of the decision.
But the Victoria and Albert Museum in London, which is leading the campaign to raise enough money to buy the statue, by the Venetian Antonio Canova, was delighted at the decision announced by Stephen Dorrell, Secretary of State for National Heritage.
A previous six-month delay in granting the licence, the latest in a series of such decisions, expired on Friday with the British fundraisers still pounds 1.8m short of the price the owners agreed with the Getty Museum in California.
The Victoria and Albert, which has pounds 4.7m pledged, and the National Gallery of Scotland, which looks certain to contribute another pounds 1.1m, feared that Mr Dorrell might let the sculpture go to the Getty Museum, which agreed to pay pounds 7.6m in 1989.
But Mr Dorrell said yesterday: 'This is a very important sculpture, it has a very special place in the affections of many people in this country and I thought it was right to provide one last period of time.
'My advisers, the Reviewing Committee on the Export of Works of Art, have 'starred' it as being of exceptional importance, for which every effort should be made to keep it in the United Kingdom.'
Mr Dorrell said he had looked carefully at what extra funds the two British galleries were likely to be able to raise within three months.
He added: ''I think there is a realistic prospect of us being able to match the Getty Museum offer.'
Malcolm Baker, acting head of research at the Victoria and Albert Museum, said: 'We are very relieved indeed and very much welcome this chance to get the remaining amount. I think there is a very good chance we will be able to.'
But Luc Hafner, the Geneva- based lawyer for the owners, said: 'I am going to ask for a judicial review of this decision because this is going too far.
'We will ask an English judge to say whether this is fair and reasonable.
'As far as we are concerned, the Government are no longer sticking to the rules, they are changing them from day to day. This has now gone on for five years. We hope that the Getty Museum will soon be the proud owner.'
The marble statue, which features the three naked daughters of Jupiter - Aglaia (Grace), Athalia (Beauty) and Euphrosyne (Joy) - was commissioned by the 6th Duke of Bedford in 1815 and arrived from Italy four years later. It remained at Woburn Abbey, the family home now run by the present Duke's son, the Marquess of Tavistock, until a few years ago. During the 1980s it was sold to Fine Art Investment and Display.