A federal judge said on Saturday that she intended to appoint an ex-top federal prosecutor who served during Donald Trump’s first term to investigate whether she was purposely misled by lawyers and administration officials over changes to a historic public golf course in Washington DC.

Jessie Liu, a former US attorney for the District of Columbia, would examine whether officials with the interior department and the National Park Service and attorneys with the Department of Justice violated ethics or misled US district judge Ana Reyes during the course of the civil case that was initiated with a lawsuit in February by the DC Preservation League and two golfers.

The lawsuit challenges one of the US president’s flurry of construction projects around the nation’s capital – in this case, the renovation of a public golf facility along the Potomac River, which is less high-profile that some of his other plans but had still riled many.

The Republican administration plans to close the East Potomac golf course and park on 15 November with the intention of constructing what it has called a “World Class, championship-level golf course that is capable of hosting major events”.

An injunction issued by Reyes last month temporarily bars the government from removing or damaging any additional trees on the course and ordered the administration to give 10 days’ notice in writing before making any “irreparable modification” to any “forms or features” of the course while the lawsuit is active.

Reyes is now giving each side a chance to be heard on her plan to name Liu as special master in the case. They must do so in writing by Friday, when the next court hearing in the dispute is scheduled.

Reyes, who was nominated by Joe Biden during his term, wants to know whether federal officials lied about the extent of renovation plans during prior months of hearings.

She also demands to know whether they were truthful about various steps they took, including cutting down hundreds of trees early last month.

Reyes announced during a hearing on 30 October that she was starting a formal investigation into the government’s conduct. Earlier in the case, she had rejected numerous motions from the plaintiffs to step in, saying she trusted the government attorneys.

As the city’s then chief federal prosecutor, Liu oversaw some of the matters referred to her office by then-special counsel Robert Mueller during his investigation into alleged ties between Trump’s 2016 election campaign and Russia.

Trump later nominated her to be associate attorney general, the third-highest-ranking justice department job. Liu withdrew from consideration after running into opposition on the Republican-led Senate judiciary committee because of her past membership in a lawyers’ group that had supported abortion rights.

David Super, a law professor at the Georgetown University law center, said the initiation of a formal investigation by a judge to look into the conduct of a trial’s participants “can be a precursor to holding someone in contempt of court”.

Super said it also is a reflection “of the difficulty she had in determining who initiated the tree-cutting in defiance of the assurances DoJ provided. She doesn’t have the time to keep holding long, complex hearings and so wants a special master to narrow the issues.”

Meanwhile, on Saturday afternoon, Trump posted a long and outlandish message on his social media platform declaring that he was “ordering” the justice department immediately to “look into” Democrats whom he said were “threatening” people in his administration with impeachment, referring to such suggested conduct as a “criminal act”.

The garbled post also accused Democrats of threatening Republican donors and called out the Michigan US senator Elissa Slotkin, a Democrat, saying she was “going after” young people who “give even the slightest inclination to be a Republican” and that this amounted to extortion. The US president did not present further detail or explanation of his claims.

The Associated Press contributed reporting