The US Congress is investigating the relations between Trump's team and Moscow, however, no evidence on alleged Kremlin's influence on the election has been provided so far.
"Witch hunt" is how Trump characterizes the probe into Russia's election interference and possible ties to his campaign associates.
On Twitter Friday, Trump wrote as part of a tweet about the probe that "I am being investigated".
Sen. Marco Rubio says it's best for the country to let the FBI's investigation into Russian Federation meddling in the 2016 presidential election take its course, and the Florida Republican tells CNN's "State of the Union" that's what he'd advise President Donald Trump.
Sekulow cited congressional testimony by fired FBI director James B. Comey that he had told Trump on several occasions that Trump was not personally under investigations.
"I do not appreciate you putting words in my mouth, when I've been crystal clear that the president is not and has not been under investigation", the attorney said.
Trump had tweeted: "I am being investigated for firing the FBI Director by the man who told me to fire the FBI Director!"
However, Sekulow's pronouncements haven't stopped Trump from once more referring to a witch hunt this morning.
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.
The president has denied that he has any nefarious ties to Russian Federation and has also disputed that he has attempted to block the investigation into his campaign's possible role in Russia's election-related hacking.More news: United States allies determined to sidestep Trump on climate
"You've now said he is being investigated after saying [he isn't]", Wallace said.
Trump has hinted that he may have taped conversations with Comey - in which the ex-FBI chief says the president pressured him for his loyalty and on the Russian Federation investigation while also urging him to drop a probe into former national security advisor Michael Flynn.
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.
Senator Marco Rubio, who lost the Republican primary election to Trump, called for a "full and credible investigation".
Asked on NBC whether Trump's social media commentary may be created to intimidate Rosenstein or Mueller, Rubio said, "I have no basis on which to make a decision on what his intent is" but added that the tweets "in no way" will impede the work of the investigation. "The FBI's going to do their job".
Comey made the existence of this investigation public in a March hearing before the House intelligence committee. "They're essentially engaging in a scorched-earth litigation strategy that is beginning with trying to discredit the prosecutor". "So he's being investigated for taking the action the attorney general and deputy attorney general recommended him to take by the agency that recommended the determination".
The president suggested on Twitter that he may have taped those conversations.
Sekulow said Trump would address the issue of the tapes - whose very existence is unclear - in the "week ahead".
The panel sent a bipartisan letter this month to White House counsel Don McGahn seeking an answer by this Friday.
The notes have been referred in the media as "the Comey memos". Schiff said if the panel can't get an answer then he believes a subpoena will be needed.
Sekulow: "He takes the action that they also, by the way, recommended".