Private tensions between US Justice Department leaders and Robert Mueller's team broke into public view in extraordinary fashion as Attorney-General William Barr pushed back at the special counsel's "snitty" complaints over his handling of the Trump-Russia investigation report.

Key points: The deep partisan divide was on display as William Barr testified at the judiciary committee

The deep partisan divide was on display as William Barr testified at the judiciary committee Mr Barr dismissed criticism by Robert Mueller about his handling of the report

Mr Barr dismissed criticism by Robert Mueller about his handling of the report Mr Barr denied misleading Congress last month about whether Mr Mueller had complained to him

Testifying for the first time since releasing the Mueller report, Mr Barr said he was surprised Mr Mueller did not reach a conclusion on whether US President Donald Trump had tried to obstruct justice, and that he had felt compelled to step in with his own judgment that the President had committed no crime.

"I'm not really sure of his reasoning," Mr Barr said of Mr Mueller's obstruction analysis, which neither accused the President of a crime nor exonerated him.

"I think that if he felt that he shouldn't go down the path of making a traditional prosecutive decision then he shouldn't have investigated. That was the time to pull up."

Attorney-General William Barr fended off criticism about his clearing of Donald Trump. ( AP: Andrew Harnik )

Mr Barr was also perturbed by a private letter Mr Mueller sent him last month complaining that the Attorney-General had not properly portrayed the special counsel's finding. Mr Barr called the note "a bit snitty".

"I said 'Bob, what's with the letter? Just pick up the phone and call me if there is an issue,'" Mr Barr said.

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The airing of disagreements over the handling of the report followed Mr Mueller's two-year investigation into Russian interference to help Mr Trump in the 2016 campaign and the possibility that his team conspired with the Russians.

During most of the investigation, the Justice Department and Mr Mueller's team seemed to be unified in approach.

Republican and Democratic politicians have been anything but unified.

And their partisan divide was on full display during the contentious Judiciary Committee hearing, which included three Democratic presidential candidates.

Some Republicans, in addition to defending Mr Trump, focused on the President's 2016 Democratic opponent Hillary Clinton's email and campaign practices and what they argued has been a lack of investigation of them.

As the hearing was getting underway, Mr Trump tweeted his familiar "NO COLLUSION, NO OBSTRUCTION." Though Mr Mueller reached no conclusion on obstruction, he did report that his probe established no collusion between the Trump team and Russia.

Democrats, for their part, moved to exploit the daylight between Mr Barr and Mr Mueller to attack the Attorney-General's credibility and accuse him of unduly spinning the special counsel's report in the President's favour.

Some also called for Mr Barr to resign, or to recuse himself from Justice Department investigations that have been spun off from Mr Mueller's probe.

They also pressed him on whether he had misled Congress last month when he professed ignorance about complaints from the special counsel's team.

Republicans like judiciary committee chairman Lindsay Graham tried to shift the focus to Hillary Clinton. ( AP: Andrew Harnik )

Mr Barr suggested he had not lied because he was in touch with Mr Mueller himself and not his team.

Mr Barr sought to minimise the rift by suggesting the special counsel's concerns were largely about process, not substance.

Mr Barr entered the hearing on the defensive following reports hours earlier that Mr Mueller had complained to him in a letter and over the phone about the way his findings were being portrayed.

Two days after receiving the special counsel's report, Mr Barr had released a four-page letter that summarised the main conclusions.

Mr Mueller's letter, dated March 27, conveyed his unhappiness that Mr Barr released what the Attorney-General saw as the bottom-line conclusions of the investigation and not the introductions and executive summaries that the special counsel's team had prepared and believed conveyed more nuance and context than Mr Barr's own letter.

Mr Mueller said he had communicated the same concern two days earlier.

"There is now public confusion about critical aspects of the results of our investigation," Mr Mueller wrote in his letter to Mr Barr.

"This threatens to undermine a central purpose for which the department appointed the special counsel: to assure full public confidence in the outcome of the investigations."

Mr Barr appeared unmoved by the criticism.

He said repeatedly that Mr Mueller had assured him that Mr Barr's letter of conclusions was not inaccurate but he simply wanted more information out.

Mr Barr said he didn't believe a piecemeal release of information was beneficial, and besides, it wasn't Mr Mueller's call to make.

The Attorney-General was asked to reappear in front of the House Judiciary Committee on Thursday (local time), but has reportedly said he will not testify again.

AP