US President Donald Trump's eldest son said he was not worried that he could be jailed over his role in the Russia probe, but suggested investigators might try to "create" legal difficulties for him.

This time it is Robert Mueller, a former FBI director who took over the high-stakes Russia probe in May after US President Donald Trump fired James Comey as FBI director.

But even without saying a word, the former FBI director and no-nonsense prosecutor has deeply unnerved the occupants of the White House just eight blocks away, especially President Donald Trump, over where his probe is going.

In an interview with the New York Times, the president also criticized Sessions' recent testimony before a Senate panel which is investigating possible collusion between Moscow and the Trump campaign, saying he had given "some bad answers."

Trump responded to reports he is personally being investigated for obstruction of justice with a characteristic scorched earth defense: claiming mistreatment of historic proportions and calling into question the probity of his accusers.

The committee said it had approved subpoenas for Cohen and for Trump's former national security advisor Michael Flynn to appear before them and supply documents.

Facing calls to resign over newly revealed meetings he held with Russia's ambassador before the election, Sessions denied any impropriety or that he lied about those encounters in his Senate confirmation hearing.