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Former President Donald Trump speaks to attendees during a campaign rally at the Johnny Mercer Theater on September 24, 2024 in Savannah, Georgia.

Donald Trump's lawyers are arguing before a federal judge that criminal charges against him related to his attempts to overturn the 2020 election should be dismissed because of the Supreme Court's ruling on how prosecutors approach obstruction cases.

The argument, presented in a new court filing Thursday, builds on arguments that have been presented to D.C. District Court Judge Tanya Chutkan for months.

Over the summer, the Supreme Court, in its U.S. v. Fischer ruling, limited how the Justice Department can use a felony obstruction charge to prosecute Jan. 6 rioters. The ruling has led Justice Department prosecutors to drop charges against a handful of those charged in the riot and has led judges to resentence the rioters.

Trump is accused of the same alleged crime: obstruction of a congressional proceeding. Trump's lawyers say the other three charges should also be dismissed.

Trump's lawyers argue that the Supreme Court's ruling requires prosecutors to not only present evidence that the congressional process certifying the election results on January 6, 2021 was compromised, but also to prove “corrupt intent.”

Prosecutors had previously said in court that Trump's case was different than that of the Jan. 6 rioters, who were affected by the Fischer verdict. They point to Trump's plan to collect fake voter certificates that would support him in battleground states and could be used to cast doubt on the certification and disrupt the transfer of power.

In a separate ruling this summer, the Supreme Court ruled that Trump is entitled to some immunity for his actions as president.

Meanwhile, Judge Chutkan gave Trump additional time to respond to special counsel Jack Smith's immunity letter, which laid out a detailed account of the federal election subversion case against the former president.

Correction: An earlier version of this post incorrectly stated that Trump's legal team is asking the federal judge to dismiss only one of the four criminal charges against the former president in this case. They asked that all charges be dismissed.

CNN's Tierney Sneed contributed to this story.