The coffin was put on the auction block late last month by a Texas funeral home owner who swapped it with Oswald's family for a new one when the body was briefly exhumed in 1981.
The top bid had reached $US37,404 ($NZ50,510) when the auction was to have closed today, but the deadline was extended by two hours after a flurry of last-minute bids poured in.
"There are a few bidders still going at it," said Nate D. Sanders, of Nate D. Sanders Auctions in Santa Monica. "We'll allow bidders to go until someone bows out."
Oswald was arrested in President John F. Kennedy's 1963 death but was slain two days later by nightclub owner Jack Ruby.
Funeral home owner Allen Baumgardner had held on to the coffin since Oswald's body was dug up in 1981 in an effort to put to rest conspiracy theories that he really wasn't buried in his grave. After the body was identified through dental records, it was returned to Rose Hill Memorial Burial Park in Fort Worth, Texas.
Because water had gotten into a cracked burial vault and damaged the original coffin, Baumgardner swapped it with Oswald's family for a new one.
The original shows signs of the water damage. Its metal ornamentation is rusted and parts of it, including the roof, have rotted. Its satin lining has long since disintegrated.
Still, the curator of a museum dedicated to Kennedy's November 22, 1963, assassination said when bidding opened on November 30 that he expected it would generate a lot of interest.
"My experience as a curator has been, if people have room and it's a Kennedy item, they will collect it," said Gary Mack, of the Sixth Floor Museum in Dallas.
The John F. Kennedy Library Foundation has declined to comment.
Baumgardner was a 21-year-old funeral home assistant when Oswald was shot to death in a Dallas police station just two days after Kennedy was assassinated while riding through Dallas in a motorcade.
"I've never seen so many security police and FBI and Secret Service and news media just everywhere," he recalled earlier this month.
