During a later appearance on "Fox News Sunday," Sekulow conceded that he could not say with absolute certainty that Trump is not being investigated because he cannot read the mind of special counsel Robert S. Mueller.
The Post reported last week that Mueller, 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.
On Twitter on Friday, Trump wrote as part of a tweet about the probe that "I am being investigated."
On Sunday, Sekulow sought to explain that Trump was using Twitter, a favorite means of communication with his supporters, to address The Post report and was not actually confirming that he is being investigated, despite writing those words.
"The president is not under investigation by the special counsel," Sekulow told NBC's Chuck Todd. "The tweet from the president was in response to the five anonymous sources that were purportedly leaking information to The Washington Post about a potential investigation of the president."
Sekulow cited recent congressional testimony by fired FBI director James B. Comey in which Comey said he had told Trump on a few occasions that Trump was not personally under investigation in relation to the Russia probe. Those conversations, however, occurred before Trump fired Comey, who was helping lead the investigation, and before the Justice Department appointed a special counsel to oversee the probe.
Last week's Post story cited five people briefed on the interview requests, who said that the current director of national intelligence, Daniel Coats, head of the National Security Agency, Mike Rogers, and Rogers' recently departed deputy, Richard Ledgett, agreed to be interviewed by Mueller's investigators.
The five people spoke on the condition of anonymity because they were not authorized to discuss the matter publicly.
Sekulow referred to The Post story as "a fake report" during an appearance on CNN's "State of the Union" on Sunday.
"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.
Other news outlets, including the Wall Street Journal, the New York Times and CNN have had similar reports since The Post broke the news Wednesday night about Trump being under investigation.
In a testy exchange on Fox, 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.
"Nothing has changed" since Comey informed the president that he was not being personally investigated, he said.
The interview turned tense, however, when host Chris Wallace then asked Sekulow about the remainder of Trump's tweet, in which Trump had complained that he was being investigated for firing Comey by the man who told him to fire Comey.
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.