"He's not afraid of the investigation-there is no investigation", Sekulow said, adding, "there is not an investigation of the President of the United States, period".
Sekulow, who is chief counsel at the American Center for Law and Justice, said that if the Post's reporting were accurate, Mr. Trump "would be under investigation for taking the action that the Department of Justice asked him to take".
"We stand by our story, which President Trump confirmed Friday in a tweet acknowledging he is under investigation for obstruction of justice", Post executive editor Martin Baron said in a statement.
Jay Sekulow, a lawyer who is part of a team hired by Mr Trump to deal with allegations of collusion by his campaign with Moscow, appeared on Sunday to contradict Mr Trump's statement on Twitter on Friday that he was being investigated for firing his Federal Bureau of Investigation director last month. "Witch Hunt", Trump said in a tweet.
Earlier on Friday, Trump said he was being investigated for firing former FBI Director James Comey. He said the "last thing we know is when he testified just a couple weeks back". Trump advisers describe the president as increasingly angry over the investigation, yelling at television sets carrying coverage and insisting he is the target of a conspiracy.
"Let me clear. The presidents not under investigation, as James Comey said in his testimony, that the president was not the target of investigation on three different occasions", Sekulow told CNN in another interview.
The president has denied that he has any nefarious ties to Russian Federation and has also disputed that he's attempted to block the investigation into his campaign's possible role in Russia's election-related hacking.
The president has directed some of his frustration at Rosenstein and Mueller.
Both Coats and Rogers declined before the Senate intelligence committee earlier this month to answer questions about their conversations with Trump, but both said they had never felt urged by Trump to intervene in the Russian Federation probes.
Sekulow referred to The Post story as "a fake report" during an appearance on CNN's "State of the Union" on Sunday.
Warrants issued for Turkish agents and others for DC protest fight
With two men arrested on Wednesday and two arrested immediately following the incident, the total number facing charges is now 18. Four people already have been charged in connection with the incident, which occurred during Erdogan's visit to the USA capital.
The Secret Service has said it has no records of any recording systems or transcripts of any conversations Mr. Trump may have had in the White House. "I can not read the mind of the special prosecutor", Sekulow said.
The president suggested on Twitter that he may have taped conversations.
Separately, a former White House lawyer, who spoke on condition of anonymity, said there was nothing stopping Trump or his lawyers from asking Mueller whether Trump was under investigation.
The panel sent a bipartisan letter this month to White House counsel Don McGahn seeking an answer by this Friday.
Wallace asked Sekulow if Trump believes that Deputy Attorney General Rod J. Rosenstein, who wrote a memo criticizing Comey's handling of the Clinton email investigation, has done anything wrong.
Schiff said if the panel can't get an answer then he believes a subpoena will be needed.
"That signifies this president knew all too well that it was inappropriate", Schiff said. Angus King, an independent from ME, stressed that the probe will likely last for a long time.
Gingrich said he had lost confidence in Mueller because he is a friend of Comey, and said too many members of Mueller's investigative team have ties to Democrats. "There's a lot of information yet to go".
In a two-part tweet posted before 7 a.m. Sunday, Trump wrote: "The MAKE AMERICA GREAT AGAIN agenda is doing very well despite the distraction of the Witch Hunt".
On CBS' "Face the Nation," host John Dickerson asked Sekulow how he knew that.