President Trump Donald John TrumpUS reimposes UN sanctions on Iran amid increasing tensions Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Trump supporters chant 'Fill that seat' at North Carolina rally MORE has sent messages through his lawyer expressing "appreciation and greetings" to special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE, Trump's chief counsel John Dowd told USA Today Tuesday.

"He appreciates what Bob Mueller is doing," Dowd said. "He asked me to share that with him and that's what I've done.

“The president has sent messages back and forth," he said.

But Trump has also publicly decried Mueller's investigation into potential ties between his campaign and Russia as a "witch hunt," and has referred to it as a "cloud" hanging over his administration.

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Dowd said the president has no problems with Mueller and that all communications between the White House and the special counsel have been proper.

“We get along well with Bob Mueller; our communications have been constructive,’’ he told USA Today. “But it is important that our communications remain confidential. It’s important that there not be any breakdown in that trust.’’

Trump came under fire for conducting private meetings with former FBI Director James Comey, whom he fired in May.

Comey recorded details of those conversations with Trump in memos, revealing to lawmakers on the Senate Intelligence Committee in June that the president once asked him for a pledge of loyalty and later pressed him to end the FBI’s investigation into former national security adviser Michael Flynn.

Mueller was appointed as special counsel to lead the Department of Justice investigation into Russia’s role in the 2016 election days after Comey was removed from office.

While Trump has repeatedly voiced frustration with the Russia probe and claimed that Mueller’s investigation would cross a line if it delved into his personal finances, Dowd told USA Today on Tuesday that notion of firing the special counsel has “never been on the table.”

“That’s never been on the table, never,’’ he said. “It’s a manifestation of the media. My dealings with Bob Mueller have always been cordial, respectful -- the way it should be."