The Post reported last week that special counsel Robert S. Mueller III, who was appointed to oversee the investigation into Russia's role in the 2016 election, is interviewing senior intelligence officials as part of a widening probe that now includes an examination of whether Trump attempted to obstruct justice.
Attorney Jay Sekulow did his best to explain to Wallace that, to his knowledge, the president is not personally being investigated.
An AP Fact Check finds that statements on the subject by both men raise questions about accuracy.
A source familiar with the Mueller probe said on Thursday that investigators would have to gather a large amount of evidence before an interview with the President would be warranted.
President Donald Trump's personal lawyer says Mr Trump is not under investigation in the probe into alleged Russian meddling in the 2016 United States presidential race, adding that the president has not received any notification that he is being investigated.
A US official who is familiar with the rough outlines of the probe and who spoke on condition of anonymity told Reuters on Thursday that Mueller was also examining whether Trump or others tried to interfere with the investigation.
Trump tweeted on Sunday morning.
"The president is not under investigation by the special counsel", said Sekulow. He said he had only been discussing the constitutional problem posed if the president were being investigated.More news: Oil slips as data points to fast-growing supply
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Sekulow then pulled out the no-nuance argument: "It was 141 characters, the limitation on Twitter as we all know".
Wallace: But you just said two times that he's being investigated.
Sekulow said that Trump, in his tweet, was reacting to a story in the Washington Post, which was the first to report that Mueller was examining whether Trump had tried to obstruct the probe by firing Federal Bureau of Investigation director James Comey in May.
The top Democrat on the House intelligence committee says the panel is looking forward to getting a response from the White House this week as to whether President Donald Trump has tapes of private conversations with fired FBI Director James Comey.
Sekulow said, "The President takes action based on numerous events including recommendations for his attorney general and deputy attorney general's office".
Sekulow: No, Chris... let me crystal clear so you completely understand. "As we know of today, the president is not under investigation". I don't think it serves him well.
Sen. Marco Rubio (R-Fla.) similarly echoed the benefits of an investigation in an appearance on CNN's State of the Union on Sunday. First of all, you've now stated that he is being investigated after saying he isn't.
"You're right, Chris. I can not read the mind of the special prosecutor", Sekulow responded.