Sekulow also cited the recent congressional testimony of former FBI Director James Comey, who said he told Trump on several occasions that he was not being personally investigated.
Trump's tweet was "in response" to a Washington Post story last Wednesday indicating that the special counsel's probe now included the president, Sekulow said in television interviews.
But Sekulow said repeatedly Sunday that "the president has not been and is not under investigation".
Mr. Sekulow said the president's tweet should not be interpreted as confirmation that he is under investigation.
Casting aspersions on the Justice Department and its inquiry, Trump on Friday seemed to confirm that he was under investigation for possible obstruction of justice by the special counsel looking into Russia's actions.
Mueller is also looking at whether, if any potential offenses were committed, Trump or others attempted to cover them up or obstruct the investigation into them, said one United States official on Thursday who is familiar with the rough outlines of the probe and who spoke on condition of anonymity.
President Donald Trump is beginning his day with a stream of tweets defending his record and lashing out at the investigation into Russian interference in the election.
President Donald Trump's announcement of a tougher line toward Cuba has delighted hardliners on the island, who say it reveals Washington's long-held aim of imposing its will on Cuba. Marco Rubio said Sunday that he does not expect Trump to seek to fire them.
"There's a limitation on Twitter, as we all know", Sekulow said.
"I don't believe it's going to happen", said Rubio on CNN's "State of the Union". "I believe this is the thing that could happen for the president".
Trump had earlier fired Flynn in February after just 24 days on the job after learning he had lied to Vice President Mike Pence about his conversations with Russian Ambassador Sergey Kislyak.
The committee sent a bipartisan letter this month to White House counsel Don McGahn seeking an answer by this Friday.
Schiff says if the panel can't get an answer then he believes a subpoena will be needed.
Rasmussen said Friday its daily presidential tracking poll that 50% of likely USA voters approve of Trump's job performance, while the other 50% disapprove. Angus King of ME, an independent who caucuses with the Democrats.
"A lot of people have said, 'When do you think you'll be done?' Maybe the end of the year". He said Trump's statement on Twitter Friday was specifically in response to a story in The Washington Post about the expanding probe into Russia's election meddling.
He spoke on ABC's "This Week".