Under a special anti-terrorism law, Japanese naval ships have been providing fuel for warships from the US and other navies operating in the Indian Ocean.
Speaking on Sunday Abe said he "would not cling to my job as prime minister" if parliament failed to back a continuation of the deployment.
Opposition parties, which won control of parliament's upper house in the vote, are against the Afghanistan mission and have threatened to delay enactment of a bill to extend it.
They say such missions violate the country's pacifist constitution.
Ichiro Ozawa, leader of the opposition Democratic Party, said Japan should only participate in UN-led peacekeeping missions.
The row over the naval deployment is the latest blow to hit Abe's government amid plummeting opinion poll ratings and a series of cabinet scandals and resignations.
Abe has vowed to push parliament to keep the Indian Ocean mission going, saying it is part of a pledge Japan has made to the rest of the world.
"I must first make every effort to obtain the understanding of the opposition parties, including the Democrats," he said on Sunday.
He said he would "put every effort possible into getting the mission extended."
The mission has been part of Tokyo's recent attempts to raise its international profile.
Under Junichiro Koizumi, the former prime minister who stepped down last year, Japan sent non-combat troops to southern Iraq to assist in US-led reconstruction efforts.