The lawsuit in U.S. District Court seeks class action status on behalf of the vehicles' owners. It was brought by John Diaz, who said his 1993 Chevrolet Astro minivan was parked blocks from the trade center.
He found it covered in soot with minor damage Sept. 11 but said he was told he couldn't remove it. He later learned his minivan was moved to a landfill.
His lawyer, Robert Tolchin, said the city has said the minivan could not be returned because it and the other vehicles towed from around the trade center were too damaged.
"We understand the city had to clear the streets to bring in heavy equipment," Tolchin said. "But once it was cleared out of the area, the people are entitled to have their cars back."
Diaz has been told his vehicle will be crushed along with the others.
The city law office did not immediately return a telephone message seeking comment.
Health Commissioner Neal Cohen said earlier this month that the vehicles are probably too contaminated with dangerous particulates to be properly cleaned.
"These vehicles are contaminated," Cohen said. "The cleanup of them is not practical, and I'll do whatever I can in my authority and recommend to the mayor that they be condemned."
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