Dowd confirmed his decision in an email Thursday to The Associated Press, saying, "I love the President and wish him well".
Dowd's departure came days after the president added to his team of lawyers Joseph diGenova, a former US attorney known for pushing a more aggressive legal strategy.
The president rebuffed these claims in a series of tweets in mid-March, saying the paper "purposely wrote a false story stating that I am unhappy with my legal team on the Russian Federation case and am going to add another lawyer to help out".
Mr Dowd had acted as the team's chief contact in dealing with Mr Mueller and has spent months carefully negotiating terms of an interview between the special counsel and Mr Trump.
On Saturday, Dowd called for an end to the investigation, which he said was manufactured by former FBI director James Comey.
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As CrimeOnline previously reported , relatives told a local newspaper that they had not heard from the family since last Thursday. Family and friends are mourning the loss of the Sharp family who were found dead in a condo in Mexico on Friday, March 23, 2018 .
Later Thursday, when Mr Trump was asked by reporters whether he still wants to testify to Mr Mueller, he said, "Yes, I would like to".
Trump intensified his criticism of Mueller last week, calling the special counsel out by name in a string of Twitter messages.
Jay Sekulow, a Trump lawyer and spokesman for the legal team, declined to comment.
Besides DiGenova and Sekulow, Trump is also represented by Ty Cobb, who works in the White House and remains on staff there.
Dowd's resignation follows reports of a possible shakeup on the president's legal team. The announcement of Dowd's exit comes just days after Trump stepped up his attacks on Mueller and his investigation. Dowd was quick to say that there had not been any decision yet about whether Trump would agree to an interview and that when that decision would be made, it would be his decision - not Trump's.
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As the weekend nears, the Syrian military is approaching a complete victory in the Damascus suburb of Eastern Ghouta . Harasta's evacuation - which began Thursday - came as part of a deal negotiated by Russian Federation.
Mueller's probe concerns unproven allegations that Trump's campaign colluded with Russians to impact the outcome of the 2016 presidential election. He said there is a "danger" for the president if diGenova undertakes a more aggressive approach with less cooperation.
On Thursday, top White House lawyer John Dowd resigned after he reportedly grew exhausted of Trump not listening to his legal advice.
This is at least the second major reshuffling of Mr Trump's legal team in the past year.
The main disagreement was that Dowd has persistently tried to get Trump to be nice to Mueller and Trump refuses to be nice to Mueller. Dowd said after that incident that he was "out of the tweeting business" and "did not mean to break news".
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Tesla said Musk recused himself from the board's vote authorizing the pay plan and did not participate in Wednesday's meeting. A company filing with the Securities and Exchange Commission showed shareholders supported the pay deal by a large margin.