Former President Donald Trump is trying to put on hold one of the January 6-related lawsuits he faces because he is now facing criminal charges.

The lawsuit accuses Trump of having responsibility for the death of Capitol Police Officer Brian Sicknick and is at an early stage. But if it moves forward, "Forcing President Trump to defend this case while simultaneously defending a criminal prosecution based on related conduct would undoubtedly compromise either his right to defend himself in this case, his criminal defense, or both," his attorneys wrote in a filing on Monday.

The lawsuit accuses Trump of causing Sicknick's wrongful death by riling up his supporters on January 6, 2021.

Sicknick was hit in the face with chemical spray and collapsed while facing the crowd outside the US Capitol during the riot. He died the next day because of a series of strokes, deemed "natural causes," a medical examiner found.

Trump's legal team wrote that the federal indictment brought against him earlier this month related to his efforts to overturn the 2020 election "overlaps substantially" with the Sicknick estate's allegations.

If Trump were to have to continue defending against Sicknick's lawsuit and it progressed to an evidence-gathering phase, he would consider asserting his Fifth Amendment rights in the lawsuit "to focus on the criminal litigation," his attorneys said.

His criminal case "at minimum raises a realistic possibility of criminal prosecution sufficient to justify the application of the Fifth Amendment," because they could provide information to criminal prosecutors, Trump's attorneys added.

Other federal lawsuits attempting to hold Trump responsible for the January 6 attack are essentially paused as a federal appeals court weighs whether he had absolute immunity as the sitting president.