The House select committee investigating the January 6 Capitol attack said in a major filing on Wednesday that it believed that Donald Trump violated multiple federal laws to overturn the 2020 election, including obstructing Congress and defrauding the United States.

The revelations came as part of a filing that intended to force John Eastman, Trump’s former lawyer, to turn over thousands of emails and records since his participation in potential crimes destroyed his arguments for attorney-client privilege protections.

The House counsel Douglas Letter said in the 61-page filing that the select committee had a basis for concluding Trump violated the law by obstructing or attempting to obstruct an official proceeding and defrauded the United States by interfering with lawful government functions.

The former president knew he had not won enough electoral college votes to win the 2020 election, yet nevertheless sought to have the then vice-president, Mike Pence, to manipulate the results in his favor, the filing said about Trump’s obstruction.

Had the effort to pressure Pence into returning Trump to power succeeded, the certification of Joe Biden’s win would have been impeded. “There is no genuine question that the president and plaintiff attempted to accomplish this specific illegal result,” the filing said.

The select committee said in the court submission that it believed Trump defrauded the United States by interfering in the certification process, disseminating false information about election fraud, and pressuring state officials to alter state election results.

House investigators also said there was evidence to suggest that the conspiracy to defraud extended to the Capitol attack, arguing it was plausible to argue Trump entered a conspiracy with the rioters to disrupt Biden’s certification on 6 January.

The Guardian first broke the news earlier this year that the select committee was investigating whether Trump oversaw a criminal conspiracy that connected the “political elements” of his scheme to return himself to office with the violence perpetrated by far-right militias.

Letter also said in the filing that the select committee believed Trump and his associates appeared to have violated the law by engaging in common law fraud as they sought to overturn the results of the 2020 election.

The select committee’s findings came as part of a 16-part court submission to persuade a federal judge to force Eastman, a central figure in Trump’s scheme to return himself to office, to at least allow the panel to confidentially review his records.

Eastman helped lead a team of lawyers at a Trump “war room” at the Willard hotel in Washington DC, which Trump called from the White House the night before the Capitol attack to discuss ways to stop Biden’s certification from taking place, the Guardian has reported.

He has so far turned over about 8,000 pages of emails and documents from 4-7 January to the panel, but has withheld an additional 11,000 documents on the basis that they are protected by attorney-client privilege or constitute confidential attorney work product.

The panel also said in the filing that Eastman’s attorney-client privilege claims were undercut by his inability to show he had been formally retained as Trump’s lawyer. An “engagement letter” that Eastman produced last week was unsigned.

Through Letter’s submission, the select committee added Eastman could not claim to assert attorney-client privilege over emails he sent on his Chapman university email server, and those messages were not protected by the attorney work product protection.

House investigators said the evidence against Trump – and Eastman’s role in counselling Trump to engage in potentially criminal activity – meant that Eastman’s claims of attorney-client privilege were destroyed by the so-called “crime-fraud exception”, among other arguments.

“The attorney-client privilege does not shield participants in a crime from an investigation into a crime,” select committee member Jamie Raskin told the Guardian. “If it did, then all you would have to do to rob a bank is bring a lawyer with you and be asking for advice.”

The select committee said that in the first instance, it simply wanted to examine Eastman’s records “in camera” – a process that takes place when a reasonable person would agree a review of the materials may help establish whether the crime-fraud exception applies.