The US Justice Department was justified when it seized the cell phone of John Eastman, a former lawyer for Donald Trump, a federal judge in New Mexico ruled on Friday.

In its investigation into a scheme by the ex-president and his lawyers to overturn the 2020 election using “fake electors”, the justice department took Eastman’s phone on 22 June as he was leaving a restaurant in New Mexico. Eastman, in turn, filed a court motion in an attempt to get his phone back, arguing that the justice department violated his constitutional rights.

Federal district court judge Robert Brack said in a court document Friday that the department had a right to seize his cell phone, noting the government had a substantial “interest in investigating the January 6 attacks on the Capitol”, which Trump’s supporters staged on the day congress certified his defeat at the hands of the Joe Biden. He noted that the justice department has said it will not go through Eastman’s phone until they get a second warrant to do so.

“The court is relying to a considerable extent on the assertion in the warrant that the investigative team will not examine the contents of the phone until it seeks a second warrant,” the ruling said. Brack gave the justice department until 27 July to update the court on whether it has applied for a second warrant.

The justice department’s investigation into the plot to overturn the election has – with help from witness testimony in the recent January 6 committee hearings on the insurrection – zeroed in on Eastman as a key figure in Trump’s 11th-hour plan to keep himself in the Oval Office.

Eastman told Trump that Mike Pence, in his role as vice-president, could single-handedly interfere with the largely symbolic certification of the electoral college that showed Biden as winner of the presidential election. Eastman and Trump tried to convince the vice-president then to hold up the proceedings, but Pence denied that he had the legal right to do so and refused to cooperate.

Pence’s legal advisers told the January 6 committee that he had to fend off mounting pressure from Eastman to go along with the plan.

“There was no basis in the constitution or laws of the United States, at all, for the theory espoused by Mr Eastman. At all. None,” Michael Luttig, a retired federal judge who served as an adviser to Pence in the weeks after the election, told the January 6 committee last month.

In a civil case involving Eastman, a federal judge said in March that it appears both Eastman and Trump committed multiple felonies as they “dishonestly conspired to obstruct the joint session of Congress on January 6 2021”.