On Sunday, however, Jay Sekulow, one of Trump's lawyers, insisted that the president’s statement did not amount to an acknowledgment that he was under investigation.
Trump’s tweet was “in response” to a Washington Post story last Wednesday indicating that the special counsel’s probe now included the president, Sekulow said in television interviews. Trump was merely restating what the Post and other media had reported, Sekulow suggested.
“Let me be very clear here, as it has been since the beginning, the president is not and has not been under investigation for obstruction,” Sekulow said on NBC’s “Meet the Press.”
Sekulow did not provide much evidence for that statement, which he repeated as he made the rounds on Sunday talk shows.
He told CBS’ “Face the Nation” that there has been no notice from the office of the special counsel, Robert S. Mueller III, that Trump is under investigation.
The FBI and federal prosecutors, however, do not routinely notify people that they are under investigation. Notification is often provided if a person has become a "target," meaning that charges could be imminent, but is not generally provided at the early stages of an investigation.
Sekulow also cited the recent congressional testimony of former FBI Director James Comey, who said he told Trump on several occasions that he was not being personally investigated. Those conversations, however, took place before Trump fired Comey -- one of the acts that could be interpreted as part of an effort to obstruct the case -- and before the Justice Department appointed Mueller.
Later, however, in an interview on "Fox News Sunday," Sekulow conceded that he could not be sure of his statement. "I cannot read the mind of the special prosecutor,” he said.
Trump's tweets have exasperated some of his aides and many of his supporters, even as they seek to defend him against what they see as a partisan investigation.
“Trump has a compulsion to counterattack. And he is very pugnacious,” former House Speaker Newt Gingrich said Sunday on ABC’s “This Week.”
“I don't think it serves him well. I don't think that tweet helped him,” Gingrich said of the remark suggesting that Trump was being investigated.
“But it's almost like it's who he has been his whole life,” Gingrich added. “I mean, he's been a fighter his whole life. He is infuriated, and legitimately, in my judgment, by this whole Russian baloney."
Other prominent Republicans expressed more support for the probe and defended the integrity of Mueller.
“The president's pretty fired up about this,” said Sen. Marco Rubio, (R- Fla.), who said he discussed the probe with Trump on Friday.
“He, from every pronouncement we have seen, feels very strongly that he did nothing wrong, and he wants people to say that, because he feels very strongly about it. I don't think that's a mystery. And he's expressing himself in that way,” Rubio said on "Meet the Press."
“That said,” Rubio added, Trump's displeasure “in no way is going to impede any of this work from continuing. It's going to happen."
"This is going to move forward. We're going to get the full truth out there," he said.
Asked if he believed that Russian agents had tried to influence the election, Rubio said he did.
"Not only do I believe it, I know it. Almost everybody else does" other than Trump, he said. "Ultimately, whether he believes it or not, the work's going to move forward," he added.
"The F.B.I. doesn't sit around all day and read tweets. The F.B.I.'s going to do their job, Mueller's going to do his job," Rubio said. "And the best thing that can happen for everybody, the president, the country, our institutions [of] the government, is for a full and thorough and credible investigation that reveals everything."
That process still has a long way to run, said Sen. Angus King of Maine, an independent who caucuses with the Democrats. King and Rubio are both members of the Senate Intelligence Committee, which is running an investigation that partially parallels the Justice Department probe being run by Mueller.
"I can say categorically that the collusion, the cooperation, aspect of the investigation is not over. And as far as that goes, I'd say we're 20% into it," King said.
"A lot of people have said, 'When do you think you'll be done?' Maybe the end of the year. This is a very complex matter, involving thousands of pages of intelligence documents, lots of witnesses. There's a lot of information yet to go."
Sekulow suggested that Trump had taken to Twitter because the president wanted to fight back against news organizations that Trump and his supporters have repeatedly accused of using leaks and anonymous sources to undermine the president.
Yet Trump’s tweets in recent days condemning the actions of his own Justice Department have reached an intense level, revealing the president's increasing agitation about the probe and the attention it has drawn.
On Sunday, Trump again called the investigation a “witch hunt.” Last week he described the concerns about Russian influence in U.S. elections as a “phony” story.