Democrats are negotiating an agreement for Robert Mueller to testify to Congress next month on his Trump-Russia investigation, according to a key committee chairman.

Representative Jerry Nadler, who heads the House judiciary committee, indicated that a deal was close in remarks to reporters in Washington on Wednesday.

Nadler said it was important to have Mueller testify “which they’ve agreed to do subject to setting a date, and we’ll see if they do that, sometime in May,” Reuters reported.

It is understood that Nadler was referring to a previous statement from William Barr, the attorney general, that he had no objection to Mueller testifying to Congress about the inquiry.

Nadler’s committee is reviewing Mueller’s investigation into Russian election interference in 2016 and possible attempts by Donald Trump to impede the investigation.

It emerged on Tuesday that Mueller wrote to Barr expressing frustration with how he characterized the conclusions of his investigation.

Mueller concluded his investigation last month and delivered a final report to Barr, spanning more than more than 400 pages. Mueller’s report, which was made public on 18 April, revealed nearly a dozen instances in which the actions of the president and his campaign may have amounted to obstruction. The report also stated that the Trump campaign was “receptive” to assistance from Moscow during the 2016 election and expected to benefit from Russian interference.

But in a letter released on 24 March – before the report came out – Barr cited Mueller’s conclusion that there was no criminal conspiracy between the Trump campaign and Moscow and declared he did not believe there was sufficient evidence to charge Trump with obstruction of justice.

Meanwhile, the top Democrat on the Senate judiciary committee requested that the panel also hold a hearing with Mueller. The California senator Dianne Feinstein said on Wednesday that she had asked the Republican committee chairman, Senator Lindsey Graham, to invite Mueller to testify. However, Graham has said he does not think the special counsel needs to appear.