Japan announced that it had sent two of its Baghdad-based diplomats to a forensic medical facility in the capital to determine whether the body parts belonged to a Japanese man seized in Iraq last week.
Two previous corpses proved not to be his.
An armed group in Iraq had on Tuesday threatened to behead Japanese backpacker Shosei Koda within 48 hours unless Japan pulled its troops out of Iraq.
Japan quickly rejected the demand.
"There is a possibility that this is the body of the Japanese hostage, but it has yet to be identified," an Iraqi Interior Ministry spokesman said after the body was discovered on Saturday.
"We are trying to find out the facts," he said.
A beheaded body found in Iraq on Friday was initially thought to be that of Koda, but was later identified as an Iraqi man.
A third corpse described as Asian-looking also turned out not to be Koda's.
The Interior Ministry spokesman said the latest body parts were found near a hospital in Baghdad wrapped in an American flag.
In a video recording aired on Aljazeera on Saturday, Polish captive Teresa Borcz Khalifa told her government that her life depended on the withdrawal of its forces from Iraq.
Teresa Borcz Khalifa asked
Poland to pull its troops out
"I am asking for help from Poland and the Polish people and whoever can help me," she said.
The video showed her sitting under the flag of the armed group that seized her last week.
At least 24 other foreigners from a dozen countries, including a British-Iraqi woman, are thought to currently be held by armed groups seeking to drive US-led forces and foreign workers out of Iraq.