Earlier reports suggested Mr Fujii's resignation had been accepted.

Mr Fujii, 77, is an experienced backer of fiscal discipline. It would be a blow to Mr Hatoyama, who took office in September, if he left.

The prime minister has promised to shift Japan to the left after half a century of conservative dominance by the Liberal Democratic Party (LDP).

Mr Fujii, who is suffering from high blood pressure, was admitted to hospital last week for tests.

He is one of only a few members of the new government with extensive previous experience of administration.

He has been seen as a champion of fiscal restraint, resisting calls from the ruling Democratic Party's (DPJ) coalition partners for more spending despite Japan's huge debt.

The prime minister is already getting a reputation for being indecisive, and is struggling to revive Japan's frail economy and tackle the vast public debt.

Mr Fujii had told reporters he was exhausted after weeks of wrangling within Japan's governing coalition to finalise the budget.

He was reported to have offered his resignation after a cabinet meeting he had left hospital to attend.

Some reports said the government had accepted Mr Fujii's resignation.

But Mr Hatoyama was quoted on January 6 as saying that he wanted Mr Fujii to see through his work on the budget.