Nunberg was sacked from the Trump campaign in 2015 after racially-charged Facebook posts he allegedly wrote came to light, though he has denied writing them.
Yet when Tur asked him if Mueller's team had anything on the president, Nunberg said, "I think they may. But he can't tell the grand Jury to get lost". "I'm not going to do it".
He then said he would reject a sweeping demand from Mr Mueller for communications between him and top Trump advisers.
The dispute over Nunberg comes as Conaway and other Republicans on the House Intelligence Committee are signaling that the panel's Russian Federation investigation is nearing an end. "You want to arrest me?"
Nunberg then went on MSNBC and two CNN shows to publicize his refusal to comply with the Mueller probe.
"I don't know what he is looking into", he told CNN.
Nunberg blurted out that he had been offered immunity in exchange for his testimony, and Melber said the claim was credible since it was allegedly made through his attorneys - and he said the offer was significant.
The President has denied he knew anything about the meeting.
Nunbert also said he thinks former Trump foreign policy adviser Carter Page worked with the Kremlin.
"The Russians and Trump did not collude", Nunberg told the Post.
A former Donald Trump adviser has sensationally implied he "may have done something wrong" during the 2016 election campaign.
During a subsequent press briefing, White House press secretary Sarah Huckabee Sanders downplayed any knowledge Nunberg may have.
"Because it is the talk out there - again, I know it's awkward - let me just give you the question so you can categorically answer", Burnett said.
Nunberg's series of interviews Monday raised concerns among some of his friends and acquaintances who described the salvo as a very public meltdown.
Another interview with Erin Burnett followed, where he was was straight-up asked if he had been drinking.
Nunberg was also the subject of a now-settled lawsuit, in which Trump sued the political consultant for $10 million and accused him of breaching a confidentiality agreement.
At the time, Nunberg's firing was viewed as part of a broader struggle between Trump aides Corey Lewandowski and Roger Stone. "I think that he may have done something during the election", Nunberg told MSNBC.
"I'm working on organizing it", he said.
Even before the Nunberg meltdown, Trump appeared fixated and angry about the Russian Federation investigation Monday, going further than before in accusing his predecessor Barack Obama of intervening in the 2016 election against him. Unprecedented. Bigger than Watergate!
Nunberg added, "The Russians and Trump did not collude".
"As we've said many times before there was no collusion with the Trump campaign".
Russian Federation denies the allegations and Trump has repeatedly insisted there was no collusion between Moscow and his campaign.
Belarus-born Anastasia Vashukevich claims she has an hour of audio recordings and photos of meetings. "At least half a dozen other CNN reporters have received similar messages", she said. But the former Trump aide is running out of legal options.