Chris Christie’s office is refusing to release emails and documents dating from the week of the “Bridgegate” scandal, it has been alleged, as the case returns to court just days before the New Hampshire primary on which the New Jersey governor has staked his presidential campaign.

Attorneys for a former Christie appointee who is battling criminal charges over the incident said in a court filing on Wednesday that they had “newly discovered” that the governor’s office had withheld “critical documents” originating from the days around the lane closures in September 2013 that gridlocked the town of Fort Lee.

Claims made by Christie’s lawyers for why these documents should be kept secret do not “pass the red face test”, according to the filing. Among the documents are emails between Christie’s press secretary Michael Drewniak and David Wildstein, a state official who has pleaded guilty to conspiracy, which were withheld on the basis of attorney-client privilege despite neither man being an attorney.

A spokesman for Christie did not respond to a request for comment.

The new allegations against Christie’s team were filed as a federal judge prepared to consider arguments in court in Newark on Friday including whether the New Jersey governor’s office should be forced to hand over thousands more emails and documents.

Attorneys for allies of the governor facing criminal charges over the Bridgegate saga are asking judge Susan Wigenton to compel prosecutors to obtain and hand over files such as Christie’s text messages, emails from his official account and any testimony he gave to a federal grand jury.

The material released by Christie’s office so far is “unintelligible, deficient, and practically useless”, one of the attorneys said in a court filing.

“We want the government to do its job, and to comply with the law the way they expect everybody else to,” the attorney, Michael Baldassare, who represents Christie’s former Port Authority deputy executive director Bill Baroni, told the Guardian on Wednesday.

The court hearing may cast a shadow over Christie’s efforts to use Tuesday’s New Hampshire primary election to revive his sputtering campaign for the Republican presidential nomination. Christie frequently claims on the campaign trail that he has been cleared of wrongdoing by several inquiries into the 2013 incident.

Baroni and Bridget Kelly, his former deputy chief of staff, are charged with conspiracy, fraud and civil rights crimes for their alleged roles in improperly shutting down access lanes to the George Washington Bridge, which connects New Jersey to New York City, for several days in September 2013.

Federal prosecutors allege that, under the guise of a traffic study, Christie aides and appointees blocked the lanes to inflict gridlock on the bridgeside town of Fort Lee, because Fort Lee’s mayor declined to endorse Christie’s re-election. Their most serious charges carry potential prison sentences of up to 20 years. Baroni and Kelly deny wrongdoing.

Wildstein, an old schoolmate of Christie’s and his second-most senior appointee on the Port Authority at the time of the bridge incident, has pleaded guilty to conspiracy, and is co-operating with prosecutors. Baroni and Kelly claim that he is lying about their involvement to help himself. In a now-notorious email at the time of the lane closures, Kelly wrote to Wildstein that it was “time for some traffic problems in Fort Lee”.

Attorneys for Kelly and Baroni are scheduled to appear in court on Friday to begin arguing that Christie’s office has not been made to release all relevant documents in the case. In a supporting court filing, Baroni’s lawyers said that at least 6,601 emails and documents have been withheld or redacted by Christie’s office. Kelly and Baroni are also requesting that the prosecutors disclose far more information about the charges against them.

Christie has been allowed to hand over emails only from his personal account, the filing said, despite it being “near impossible to conclude that there are no emails from the governor’s work email address related to the lane closures”.

Baroni’s defence team also said Christie’s office had wrongly asserted that many documents are protected by privilege, and released an unusable jumble of more than 17,000 unordered pages as a single PDF. It “seems as though documents were gathered from the governor’s office, dropped from a rooftop and, after gathering them willy-nilly, given to the government,” the filing said.

Christie, who was once hailed as a formidable contender for the Republican presidential nomination, suffered a sharp downturn in popularity following the bridge fiasco and now consistently scores single-digit poll ratings. He finished 10th in Monday’s Iowa caucuses after receiving the support of less than 2% of caucus-goers. Allies have long maintained that as a relative moderate he is better positioned to succeed in New Hampshire, whose primary voters cast ballots on Tuesday. An aggregate of polls in the state by RealClearPolitics, however, currently places him in sixth place with 6.2% of support.

Despite the allegations that he is withholding emails in the Bridgegate case, Christie has on the primary campaign trail repeatedly attacked Hillary Clinton for her use of a private email account for all her government business.

Speaking in Iowa last week, Christie tried to play down the significance of his own controversy. “This was not a murder,” he said. “This was a traffic jam.”

He then repeated a claim that he had been formally exonerated several times. “It’s been investigated by three different agencies, two of them led by Democrats, they all concluded the same thing: that I had nothing to do with it,” he said, according to the Newark Star-Ledger.

In fact, as the newspaper pointed out this week, neither of the official inquiries into the scandal – one by US attorney Paul Fishman, the other by the state legislature – has announced any such conclusion.

The one report that did clear Christie was a review by his own lawyers, which cost New Jersey taxpayers an estimated $8m.

In a ruling issued in December, judge Wigenton sharply criticised the inquiry, accusing Christie’s lawyers at the firm Gibson, Dunn & Crutcher of “opacity and gamesmanship” after it emerged that they had not kept notes of interviews.

In their own motion to be discussed on Friday, Kelly’s attorneys accused prosecutors of carrying out a “massive electronic document dump” of 1.7m pages that were unsearchable. They complained to the judge that it would take three years for three attorneys each working 50 hours a week to read all the material.

In a 59-page filing rejecting the claims of Baroni and Kelly that they were entitled to more information, government prosecutors said they had “provided extensive discovery” material. William Skaggs, a spokesman for the US attorney’s office in New Jersey, said on Wednesday: “We won’t be commenting any further than what we have filed.”