Christine Lagarde aims to be first female IMF chief

Announcing her intention to run, Ms Lagarde said she would bring her experience as "a lawyer, a minister, a manager and a woman" to the post of managing director.

She is seen as a clear front-runner to replace Strauss-Kahn, who is facing prosecution in New York over charges that he attempted to rape a maid in his hotel suite.

The former IMF boss was released on bail last week after posting a combined $6 million (about 3.7m) cash and insurance-backed bond.

He remains under house arrest, with an electronic tag monitoring his movements and an armed guard placed at his residence.

Strauss-Kahn faces counts of committing criminal sexual acts, attempted rape, sex abuse, forcible touching and unlawful imprisonment.

It is alleged that the 62-year-old Frenchman chased the cleaner down the corridor of his hotel suite before sexually assaulting her.

In court last week, assistant district attorney John McConnell said the alleged victim had provided a "compelling and unwavering" story and that a physical examination had backed up her claims.

It is believed that Strauss-Kahn's DNA matches material found on the maid's uniform.

It has also been claimed that friends of the accused man approached the hotel worker's family in her native Guinea in an attempt to buy her silence.

It was reported that a seven-figure sum was being discussed by contacts of Strauss-Kahn in an attempt to secure his freedom.

The French politician stepped down from the IMF last week, pledging to clear his name.

Following the resignation, Ms Lagarde, 55, emerged as a leading contender to take over at the top of the organisation.

Tradition dictates that a European heads up the IMF, while an American always presides over its sister body, the World Bank.

A number of countries have already backed Ms Lagarde's bid to replace Strauss Kahn. In Britain, Chancellor George Osborne has described his French counterpart as an "outstanding candidate".

Ms Lagarde's formal announcement was made yesterday, after consultation with French president Nicolas Sarkozy.

The French finance minister has won plaudits for her handling of the European financial crisis – many credit her with negotiating rescue deals for debt-hit Greece, Ireland and Portugal.

But her candidacy is not being backed by all.

On Tuesday, a coalition of some the world's biggest emerging-market nations called for an end to the "obsolete" convention that a European should always head the IMF.

In a joint statement, board directors from Russia, India, China, South Africa and Brazil said the unwritten rule "undermines the legitimacy of the Fund".

Ms Lagarde also faces problems at home. The finance minister is embroiled in a long-running controversy over compensation paid by the state to a prominent backer of Mr Sarkozy.

In 2008, Ms Lagarde sent a dispute between businessman Bernard Tapie and bailed-out bank Credit Lyonnais to arbitration.

Mr Tapie claimed failings by the lender over the acquisition and subsequent sale of sportswear company Adidas. An arbitration panel eventually awarded €285m (about 25m) in taxpayers' money to Mr Tapie.

Opponents claim Ms Lagarde abused her authority in referring the dispute to arbitration. Next month, a French court is due to decide if it is to launch an official investigation into the case.

The IMF is expected to announce Strauss-Kahn's replacement by the end of June.