Trump said last month he planned to seek Chutkan's recusal as well as a change of venue for the case.
Trump argued in a court filing that Chutkan's prior statements appearing to refer to Trump's role in influencing the January 6, 2021 attack on the US Capitol by his supporters raise questions about her impartiality in the case.
The court filing cites a remark Chutkan made at a 2022 sentencing hearing for a Capitol riot defendant in which she suggested that the rioter was motivated by "blind loyalty to one person who, by the way, remains free to this day."
Trump's lawyers argued that the comment indicated the judge's belief that Trump "should be prosecuted and imprisoned."
Trump has been charged by US Special Counsel Jack Smith with four felony counts for allegedly plotting to subvert the results of the 2020 election. That is one of four criminal cases he faces as he runs for the Republican nomination in 2024. He has pleaded not guilty to all charges.
"Although Judge Chutkan may genuinely intend to give President Trump a fair trial - and may believe that she can do so - her public statements unavoidably taint these proceedings, regardless of outcome," Trump's lawyers wrote.
Trump has frequently criticised Chutkan on his social media site since she was randomly assigned to preside over the election case in Washington federal court.
Chutkan set a trial date in the case for March 2024 over the objections of Trump and his lawyers, who sought to push the proceeding back to 2026. The judge also previously warned Trump about attempting to influence potential witnesses in the case.
The Washington indictment does not specifically charge Trump for the Jan. 6 attack, but alleges that he exploited the riot in an attempt to delay Congress' certification of his defeat by Democrat Joe Biden.
Chutkan, who was nominated by former Democratic President Barack Obama, ruled against Trump in 2021 in a civil case he brought attempting to shield his White House records from the US House committee that investigated the Capitol attack.
"Presidents are not kings, and plaintiff is not president," Chutkan wrote in her ruling.
Trump also on Monday sought to dismiss seven of the counts he faces in a separate Georgia case, arguing that he is immune from prosecution for actions he took in his official capacity as president.
