Kaczynski, who pleaded guilty in 1998 to setting 16 explosions that killed three people and is serving a life sentence in federal prison, has declined to voluntarily provide a DNA sample.
Chicago FBI spokeswoman Cynthia Yates declined to say whether the agency would try to compel him to give one. She said the FBI is pursuing DNA from "numerous individuals" in the investigation, but declined to provide details about any of the others.
The U.S. Marshals Service is currently auctioning off items seized from Kaczynski's home. Ahead of that auction, he filed a motion asking California courts to order the government to keep certain items taken from his cabin in 1996, including journals that could prove his whereabouts in 1982 and other evidence that could clear him in the Tylenol case.
In a response filed Monday, federal prosecutors said the courts lack the jurisdiction to enter such an order and note that Kaczynski hasn't been indicted in connection with the Tylenol investigation "and no such federal prosecution is currently planned."
Kaczynski, who's in federal prison in Colorado, said in his motion that the officials who notified him of the FBI's request said the agency was prepared to get a court order to compel him to provide a DNA sample. He said he would provide one "if the FBI would satisfy a certain condition that is not relevant here," but doesn't elaborate.
The Tylenol case involved the use of potassium cyanide and resulted in a mass recall. Kaczynski said he has "never even possessed any potassium cyanide."
In a space of three days beginning Sept. 29, 1982, seven people who took cyanide-laced Tylenol in Chicago and four suburbs died. The deaths triggered a national scare and a huge recall, and eventually led to the widespread adoption of tamperproof packaging for over-the-counter drugs.
In 2009, federal agents searched the Boston home of James W. Lewis, who served more than 12 years in prison for sending an extortion note to Tylenol maker Johnson & Johnson demanding $1 million to "stop the killing." Lewis has denied being involved in the poisonings.
No charges have ever been filed in the deaths.