50-year-old Rana was acquitted of federal charges that he aided the terrorists who carried out the attacks in Mumbai after an eight-day trial in Chicago earlier this year but was convicted for the Danish plot.
He was convicted of providing material support to the banned Lashkar-e-Taiba, and of conspiracy to provide material support to terrorism in connection with a separate, foiled plot involving the Danish newspaper- Jyllands Posten.
Rana's lawyers, led by defense attorney Patrick Blegen, argue in new federal court filings that Rana should be granted another trial because if the Mumbai evidence were not put before jurors, the panel would not have convicted him on the other counts, the ''Chicago Sun-Times'' daily said.
"Rana should not have been forced to defend the Mumbai and Denmark plots simultaneously," Rana's lawyers wrote.
"Charges of involvement in a single terrorist plot creates immense fear, prejudice, and the risk of emotion overwhelming a jury even in the best of circumstances.
"Forcing a defendant to defend two terrorist plots simultaneously is simply untenable."
The daily said the lawyers also argue that the convictions should be thrown out because the bulk of the government's evidence came from e-mails, recorded telephone calls and recorded conversations that they had access to under the Foreign Intelligence Surveillance Act.
Rana's lawyers say that the act is supposed to be used to collect intelligence, not for criminal prosecutions.
Rana faces up to 30 years in prison for the plot to attack the Danish daily for publishing caricatures of Prophet Mohammad and has been in custody since his October 2009 arrest. The trial had also featured the testimony of his Pakistan born American terrorist friend David Headley.