The answers represent the first time Trump has given his own version of events to the special counsel's team in the 11 months ago since Mueller first asked for a sit-down interview with the president.
Last August, Trump lawyer Rudy Giuliani said he had discouraged Trump from testifying out of concern for a "perjury trap" Mueller might set.. While it helps Trump avoid the pressures and quick thinking in-person follow-ups demand, it also binds him to testimony just as legally binding as if he gave it to Mueller directly.
One of Trump's attorneys said the answers will not provide any great surprises.
Trump's submission comes almost a year after Mueller, a former Federal Bureau of Investigation director, first indicated to his legal team that he was interested in questioning the president, the Wall Street Journal said. He said Mueller's office had received "unprecedented cooperation from the White House", including about 1.4 million pages of materials.
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The issues Trump covered in his responses are "the Russia-related topics of the inquiry", Sekulow said. If it doesn't, you know, I'll be told and we'll make a decision at that time.
Mueller was tasked to probe "any matters that arose or may arise directly from the investigation" into possible collusion between Trump's campaign and Russian Federation during the 2016 election. Moscow has said it did not interfere in the election and Trump has denied any collusion.
President Trump told reporters Tuesday at the White House that he had handed his lawyers "the written answers to the witch hunt that's been going on forever".
Mr Trump - who has repeatedly criticised Mueller's investigation, which is especially concerned with whether his campaign colluded with Russian Federation - also confirmed that the written answers had been completed.
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Trump last summer denied knowing about the Trump Tower meeting with the Russians, who had promised damaging information about Democratic rival Hillary Clinton.
"It is time to bring this inquiry to a conclusion", Giuliani said.
Other questions may have touched on WikiLeaks founder Julian Assange and Roger Stone, a longtime Trump ally with ties to WikiLeaks, who also is under investigation.
Giuliani added, however, that an obstruction-of-justice subpoena from Mueller could only cover information that he has no other way of obtaining.
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Mueller has already has brought charges against some former Trump aides, including his former campaign chairman and his former national security adviser, as well as a number of Russian individuals and entities. "But probably this is the end", said the president, who has regularly dismissed the probe as a "witch hunt" and personally slammed Mueller.