Trump tweeted: "Russian officials must be laughing at the United States a how a lame excuse for why the Dems lost the election has taken over the fake news".
In a resignation note to friends and colleagues, Dubke said it was his "distinct pleasure to work side-by-side, day-by-day with the staff of the communications and press departments".
According to Priebus, Dubke "will remain on board until a transition is concluded".
A parallel can be made between the early struggles of the Trump administration and the first year of the Bill Clinton presidency.
He was previously a Republican strategist who founded Crossroads Media and had long ties to party establishment figures, including strategist Karl Rove.
Mr. Trump certainly needs to fix his White House mess, but staff changes won't matter unless the President accepts that he is the root of the dysfunction. Dubke's tenure is open-ended and it's unclear if he'll officially depart the White House before a successor is named.
Stop the average person on the street and ask them if they know the name "Mike Dubke" and you are nearly certain to get a blank stare.
Schapelle Corby lands in Australia
As Corby remained holed up in her Kuta villa in the days before "D-day", as it is known here, anticipation built to a fever pitch. Now a free woman, the 39-year-old who once described the media as exploitative began posting images on instagram on Saturday.
Dubke joined the administration in February after he was brought in by Sean Spicer, who served as both press secretary and communications director in the opening days of the Trump administration.
"When that strategy is complete, we'll have something for you on it", White House Press Secretary Sean Spicer told reporters on Tuesday at his daily news conference, the first after the return of President Donald Trump from his maiden overseas trip.
In the past month, the President's communications team has been working on the frontlines of the administration to deal with the fallout from Mr Trump's firing of FBI Director James Comey, alleged "leaks", the President's disclosure of classified information to Russian officials, and Mr Trump's potential obstruction of justice by asking Mr Comey to drop an FBI investigation into former National Security Advisor Michael Flynn.
Kushner "has a strong team around him working on every part of his portfolio", a source close to Trump's son-in-law said, adding he wasn't planning on leaving, at least of his own volition.
Embassies scrambling to build contacts with Trump's new administration were quick to realise Kushner's pivotal role as a trusted ambassador and facilitator - but also a presidential family member who would survive the inevitable White House knife fights. The person wasn't authorized to publicly discuss private policy deliberations and insisted on anonymity. In an interview with ABC News' Martha Raddatz, Rep. Adam Schiff (D-Calif.), the House Intelligence Committee's top Democrat, has called for a review of Kushner's security clearance following reports that he sought to establish a "backchannel" with Russian officials.
Republican and Democratic operatives in recent days have said the problem with a West Wing makeover will be finding qualified and capable Republican hands who are willing to work for a president and administration that are under federal and congressional investigation - and that have struggled to produce clear domestic victories while also angering longtime US allies like Germany.
"I honestly can't say that it's going to be a wave", one official said, speaking on condition of anonymity to discuss internal matters at the White House.