During an interview on NBC's "Meet the Press" Jay Sekulow, a member of Trump's legal team, said the president was specifically tweeting about the reports that he was under investigation and insisted that Trump had not been notified of any investigation.
On "Fox News Sunday", Sekulow said that he was certain the president was not under investigation because he had received no notification or other indication that he was.
Sekulow, chief counsel for the American Center for Law and Justice, said the president was only referring to a news report.
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.
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.
Sekulow: No, Chris... let me crystal clear so you completely understand. "That the president was not and is not a target of investigation".
Sekulow claimed the president is not spending a lot of time composing the tweets, but defended them as a means of speaking directly to voters, saying "he's responding to what he's seeing in the media in a way in which he thinks is appropriate to talk to those people that put him in office".
In a combative and testy exchange on "Fox News Sunday", Sekulow acknowledged he could not know for sure that Mueller has not opened an investigation, but said he had no reason to believe he had.
Schiff said Trump, his legal team and his supporters were trying to discredit the special counsel and his investigation. "He's being investigated for taking the action that the attorney general and deputy attorney general recommended him to take by the agency who recommended the terminations!"
The panel sent a bipartisan letter this month to White House counsel Don McGahn seeking an answer by this Friday.
Trump has denied any collusion between his campaign and Russian Federation. It also sent a letter to Comey asking for any notes or memos. Sekulow said that Trump would have challenged the basic assertion of the article, but was constrained by Twitter's limit of 140 characters per post.
Schiff said if the panel can't get an answer then he believes a subpoena will be needed. Schiff cited the fact that the president at one meeting "cleared the room" of advisers and asked to speak to Comey alone. Trump appeared to acknowledge that he was a target of the probe when he tweeted about it.
And Senate intelligence committee member Sen. King said the "collusion, the cooperation aspect of the investigation is not over".
He spoke on ABC's "This Week".