The president also in one of his many tweets Saturday morning brought up his power to issue pardons, apparently in the context of the Russia probe.
Trump's highlighting his power as president to issue pardons comes on the heels of his legal team's asserting that the question of pardons related to the Russia investigation is "not on the table."
Sekulow's comment came in response to a Washington Post report Friday that Trump was asking people on his team about the extent of his ability as president to pardon people in relation to the special counsel investigation into Russian interference in the election and possible collusion with members of the Trump campaign.
The president also in his Twitter rant Saturday defended his son, Donald Trump Jr., who has come under scrutiny for his meeting with a Russian lawyer during the election, and returned to a campaign theme on alleged wrongs by Hillary Clinton and her associates.
In contrast to President Trump's ongoing criticism of the nation's news media, which he often calls "fake news," former CIA Director John Brennan in his remarks at the Aspen Security Forum on Friday night said a free press is "one of the real foundational pillars" of U.S. democracy and the intelligence community has a responsibility to defend it.
"The effort to delegitimize the press and the media ... is something that we should not ever allow," said Brennan, who headed the CIA under President Obama. "Part of what the intelligence community's mission was, was to make sure that this great country can have a free and open press. And it's something that we have fought for and many people have died for."
ABC News' Mike Levine contributed to this report.