Japan's government has extended the parliamentary session into the new year for the first time in 14 years, in an effort to pass a controversial bill.
Mr Fukuda has rejected rumours of an impending election
Opposition MPs, who control the upper house, are blocking the bill, which would allow Japan to refuel US warships involved in conflict in Afghanistan.
But Prime Minister Yasuo Fukuda is determined to secure a renewal for the mandate of the refuelling mission.
Analysts say the stand-off may damage Japan's security alliance with the US.
Japanese vessels that had been supporting US-led coalition warships in the Indian Ocean returned home at the end of October, when the mandate for their mission expired.
The opposition's continued refusal to approve the bill is causing Mr Fukuda severe problems, says the BBC's Chris Hogg in Tokyo.
While deliberations continue, it is hard for him to get anything else through Japan's parliament, the Diet.
And he is also finding it difficult to leave Japan on trips he wants to make to China and to Europe, our correspondent adds.
But he says he will not back down and he has rebuffed rumours that he is about to call a snap election to defuse the situation.
"It is not the time to think of dissolving the lower house now," he told reporters.
The opposition can delay the bill for only 60 days - until mid-January.
After that Mr Fukuda is expected to force it through parliament with a rarely used procedure that will ensure it becomes law.