MUMBAI (AFP) - India's rupee and stocks jumped on Thursday after the new central bank governor Raghuram Rajan outlined a reform plan aimed at boosting the ailing currency and slumping economy.

The rupee strengthened to 65.75 against the dollar in early trade, gaining nearly two percent from its previous close, on investor hopes that the worst could be over for the currency.

Indian shares jumped nearly 2.5 percent to 19,025.74 points, led by banking stocks, after Rajan took over Wednesday from Duvvuri Subbarao as head of the Reserve Bank of India (RBI).

He sought to reassure rattled markets with his first speech in the post, outlining a new approach to the currency crisis and warning that he may have to take unpopular steps to get Asia's third largest economy back on track.

Mr Rajan, a former IMF chief economist, stressed he would hew to the RBI's mandate of "securing monetary stability" and sustaining confidence in the value of the country's money, which means "low and stable inflation".

India faces its worst financial crisis in decades, as the once-booming economy grapples with sharply slowing growth, high inflation and a record current account deficit.

Some analysts fear the economy could be heading for a meltdown with the rupee down around 22 percent against the dollar this year.

Mr Rajan's big-bang entry to the job, which included pledges to liberalise financial markets, find ways to inject capital into the markets and remove curbs on domestic banks opening new branches, received rave reviews from economists and the local media.

"This was easily the most substantive speech by a Reserve Bank governor on his first day in office," financial daily Business Standard said on Thursday.

Mr Rajan, famed for forecasting the 2008 global financial crisis, left his post as a professor at the prestigious University of Chicago's Booth School of Business and returned to India last year before taking up the new job.