Donald Trump on Wednesday afternoon postponed a planned meeting with deputy attorney general Rod Rosenstein, amid uncertainty over his future at the Department of Justice. The meeting now looks likely to take place next week.

The White House issued a statement saying the administration did not want to “interfere” with the public hearing on Capitol Hill taking place on Thursday, involving the supreme court nominee Brett Kavanaugh and a woman who has accused him of sexual assault as a teen, Dr Christine Blasey Ford.

The president had been due to meet Rosenstein at the White House on Thursday, following reports that the DoJ’s second-highest official had offered to resign last week – and had faced being fired – after an account emerged of him reportedly discussing whether Trump should be removed from office.

Trump pointed out on Wednesday that Rosenstein had denied making such remarks, first attributed to him in a New York Times report, including that he had discussed possibly secretly recording the president and using the constitution’s 25th amendment to remove Trump from office in 2017, early in the administration.

“I would much prefer keeping Rod Rosenstein,” Trump said at a news conference in New York. “He said he did not say it. He said he does not believe that. He said he has a lot of respect for me, and he was very nice and we’ll see.”

Trump added: “My preference would be to keep him and to let him finish up.”

Rosenstein is overseeing the special counsel Robert Mueller’s investigation into Russian interference in the 2016 election and allegations of improper connections between the Trump election campaign and Moscow, and his dismissal would put that investigation in jeopardy and create a political storm.

On Thursday morning, as most of Washington – and the country – was glued to the dramatic hearing of the Senate judiciary committee on Kavanaugh, the Rosenstein meeting, which Trump had said earlier in the week would take place on the same day, was in the balance.

Then, just as the hearing was about to break for lunch, the White House press secretary, Sarah Sanders, issued a statement saying that Trump “spoke with Rod Rosenstein a few minutes ago and the plan to meet next week. They do not want to do anything to interfere with the hearing.”