Ozawa says he is against the refuelling mission as it is not under a United Nations mandate.
But he has said a solution was possible "if we can find common ground over our ideals and principles".
"If this continues, the government's hands will remain tied in all matters of decision-making"
Nobutaka Machimura, chief cabinet secretary
Fukuda, who took over as prime minister in September, said Tokyo must continue to back Washington or risk being sidelined in its so-called "war on terror".
As a compromise, the government proposed scaling down the mission to prevent its fuel from being used for combat in Afghanistan, limiting Japan to the role of assisting ships on patrols.
Nobutaka Machimura, chief cabinet secretary, said he hoped the two could break the deadlock.
"If this situation continues, the government's hands will remain tied in
all matters of national decision-making," he said. "I hope we see progress."
The two ships in the mission – a destroyer and a refueller with 340 troops aboard – were due to head back home on Thursday.
The US state department said the US will continue to push for an early revival of Japan's refuelling mission.
"While we are disappointed that these refuelling activities have temporarily been halted, we certainly hope that the new legislation will move through the Japanese system quickly," Tom Casey, a spokesman, said.
Japan has provided about 126 million gallons of fuel worth $520m to coalition warships in the Indian Ocean, including those from the US, Britain and Pakistan.