(CNN) Senate Democrats grew increasingly incredulous and visibly frustrated Wednesday with intelligence chiefs testifying at a hearing after Director of National Intelligence Dan Coats and NSA Director Adm. Mike Rogers repeatedly said they would not discuss their private conversations with President Donald Trump.

Coats and Rogers said they did not feel the public setting of the Senate intelligence committee's hearing was an appropriate venue to discuss their conversations with Trump, which have reportedly included talk of the FBI investigation into former national security adviser Michael Flynn.

But that did not satisfy Democrats, who said there was no reason for them not to divulge the details.

"Director Coats, you've said as well that it would be inappropriate to answer a simple question about whether the President asked for your assistance in blunting the Russian investigation," said Sen. Martin Heinrich, a New Mexico Democrat. "I don't care how you felt. I'm not asking whether you felt pressured. I'm simply asking did that conversation occur?

"And once again, senator, I will say that I do believe it's inappropriate for me to discuss that in an open session," Coats responded.

"You can clear an awful lot up by simply saying it never happened," Heinrich later said.

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"I do not share with the general public conversations that I have with the President or many of my colleagues within the administration that I believe should not be shared," Coats repeated.

"Well, I think your unwillingness to answer a very basic question speaks volumes," Heinrich said.

Sen. Angus King of Maine, an Independent who caucuses with Democrats, picked up on Heinrich's questions, demanding a "legal justification" for why Rogers and Coats were not answering questions.

"Why are you not answering the questions? Is there an invocation of executive privilege?" King asked.

"Not that I'm aware of — because I feel it's inappropriate," Rogers said.

"What you feel isn't relevant, admiral," King shot back. "The question is why are you not answering the question?"

King also went after acting FBI Director Andrew McCabe for invoking the probe of special counsel Robert Mueller, when McCabe said he wouldn't comment on issues in the special counsel's lane.

"I don't understand why the special counsel's lane takes precedence over the land of the United States Congress" King responded.

Virginia Sen. Mark Warner, the top Democrat on the Senate Intelligence Committee, tried to push back on that argument, asking whether Mueller has told the witnesses they should not testify.

"If you've not had questions waived off with Mr. Mueller, I think frankly — and I understand your commitment to the administration — but Sen. King, Sen. Heinrich and my questions deserve answers, and at some point the American public deserve full answers," Warner said.

Deputy Attorney General Rod Rosenstein responded that when there's a Justice Department investigation, their default position is not to discuss that publicly.

"Is that the rule for the President of the United States as well?" Warner responded. "Because that is what the questions are being asked about, reports that nobody has laid to rest here that the President intervened directly in an ongoing FBI investigation. And we've gotten no answer from any of you."

During California Democratic Sen. Kamala Harris' questioning of Rosenstein, Sens. John McCain and Intelligence Chairman Richard Burr both spoke up to tell her to give the witnesses a chance to answer her questions.

"The chair is going to exercise the right to allow the witnesses to answer the question," Burr said after cutting off Harris' questions. "And the committee is on notice to provide the witnesses the courtesy — which has not been extended all the way across — extend the courtesy for questions to get answers."

In an interview on CNN's "Erin Burnett OutFront" following the hearing, Republican Sen. Susan Collins joined her Democratic colleagues taking issue with the lack of answers from Coats and Rogers.

"There was no assertion of executive privilege, and thus I don't understand why these individuals did not answer all of our questions today," Collins said. "If the special counsel Bob Mueller had put constraints on them, or if the President had made the mistake of asserting executive privilege, then I would've understood their failure to respond."

She said it appeared the intelligence officials were in a "limbo" where executive privilege had been discussed, but not yet decided on.

Wednesday's hearing was not scheduled to discuss the Russia investigation, and both Coats and Rogers indicated they might be more forthcoming in a classified setting with an intelligence panel.

There was a classified session for Wednesday's hearing scheduled for the afternoon, but the witnesses were not among those supposed to appear.

Democratic Sen. Joe Manchin of West Virginia asked if they could show up in the SCIF, the secure facility for classified hearings, but Intelligence Chairman Richard Burr said that was not an option.

"I think we need you in the SCIF sooner than later," Manchin said.