Nichols was convicted of involuntary manslaughter and conspiracy charges in the bombing, which killed 168 and injured more than 500.
Nichols is asking U.S. District Judge Richard P. Matsch, who heard Nichols' case in Denver, to vacate his conviction and sentence.
Attorneys for Nichols said he deserves a new trial because the jury that found him guilty of eight counts of involuntary manslaughter was not properly instructed on the charge of conspiracy to use a weapon of mass destruction.
Prosecutors disputed Nichols' argument that the conspiracy law he was convicted of violating was unconstitutional and that an FBI scientist should have been allowed to testify as a rebuttal defense witness.
In documents filed in federal court, defense lawyer John M.
Richilano reasserted Nichols' argument that the conspiracy law is unconstitutional because it allows a judge, instead of a jury, to assess facts that could result in the death penalty.
Prosecutors said Nichols' argument is irrelevant because he received a life sentence, which the conspiracy statute allows independently of considerations of the death sentence.
Richilano argued that the statute was unconstitutional because it exposes the defendant to the possibility of a death sentence without a jury making that decision.
Richilano also disputed prosecutors' argument that an appeals court had already upheld the exclusion of FBI scientist Frederick Whitehurst as a witness.
Richilano said an appeals court had ruled only against Nichols'
claim that he had been denied his rights under the Sixth Amendment to the Constitution.
He said the appeals court had not ruled on Nichols' claim that the exclusion of Whitehurst violated his Fifth Amendment right to present a defense.
Richilano argued that the right to present defense witnesses is fundamental, and "the right to present an expert defense witness, to rebut two key government experts upon whom the prosecution's case heavily relied, is all the more fundamental."
In December, Nichols lost another bid for a new trial after a federal appeals court ruled the FBI did not withhold crucial evidence.
The court also rejected Nichols' request to look at more of the 43,000 lead sheets developed by the government during the investigation, saying Nichols failed to prove they would help his case.
Nichols also faces a separate trial on state murder charges in Oklahoma.