"I love the president and wish him well," Dowd told NBC News.
Dowd's resignation comes only two days after he told CNBC "No" when asked whether Trump would be soon making changes to his legal team, as The New York Times had reported Monday.
The Times, which also broke the news of Dowd's departure, noted that he had been considering leaving in recent months, after having been tapped to head Trump's legal team last summer.
Dowd thought that Trump was increasingly ignoring his legal advice, the Times said, citing a person briefed on Dowd's departure.
Specifically, Dowd opposed Trump's desire to be interviewed by Mueller's office.
In a statement after Dowd's resignation announcement, another Trump lawyer, Jay Sekulow, said: "We will continue our ongoing representation of the President and our cooperation with the Office of Special Counsel."
He added: "John Dowd is a friend and has been a valuable member of our legal team."
Two sources close to the president's legal team told NBC News that Trump is interested in bringing back his previous lead lawyer for the Russia probe, Marc Kasowitz, who was removed last summer.
Kasowitz, who is currently representing Trump in a defamation lawsuit filed in New York state court by an ex-"Apprentice" contestant who claims Trump sexually groped her, "is someone the president can trust" as he grows anxious about the Mueller probe, according to NBC News.
Last weekend, Dowd called on Deputy Attorney General Rod Rosenstein, who has oversight over the Russian probe because of Attorney General Jeff Session's recusal, to end that investigation by Mueller's office.
The Times reported that Trump was angry that Dowd, who had originally claimed to be speaking on the president's behalf in that call, had backtracked by claiming he was actually not speaking for Trump.
Mueller is investigating the role Russians played in trying to illegally influence the presidential election and is looking into whether associates of Trump colluded with Russians.
Trump has repeatedly denied any collusion with Russia.
The president has also scoffed at reports that he was unhappy with Dowd.
Dowd is leaving just three days after former federal prosecutor Joseph diGenova was added to Trump's legal team for that probe.
DiGenova has claimed, without providing solid evidence, that the FBI and Justice Department cooked up evidence to make Trump look bad in an effort to help the presidential candidacy of Hillary Clinton.
"There was a brazen plot to illegally exonerate Hillary Clinton and, if she didn't win the election, to then frame Donald Trump with a falsely created crime," diGenova told Fox News in January.
"Make no mistake about it: A group of FBI and DOJ people were trying to frame Donald Trump of a falsely created crime."
On Tuesday, after a Washington Post report that Trump wanted to add high-powered lawyer Theodore Olson to his legal team, a partner at Olson's firm tweeted that Olson would not be representing the president.
Other top-tier attorneys, such as Robert Bennett and Emmet Flood, both of whom represented President Bill Clinton, have reportedly turned down chances to join Trump's defense team.
Last week, the Federal Election Commission notified Trump's 2020 presidential campaign that Dowd was one of 108 donors to that campaign who had given more money than is legally allowed.
Dowd had contributed $3,000, which is $300 above the limit, according to the FEC's tally.
Trump campaign treasurer Bradley Crate told CNBC the campaign had sent Dowd refund check for the $300 in January, after the time period whose records were cited by the FEC.
— Additional reporting by CNBC's Eamon Javers