Senator Ron Wyden said Sessions was "stonewalling," and the public was frustrated by it.
The President undoubtedly has the right to assert executive privilege and stop an adviser from revealing details of deliberations, and Justice Department policies on releasing information to the public note the concept of "deliberative process privilege," which is meant to "encourage open, frank discussions on matters of policy between subordinates and superiors".
Legal analysts, though, were split on whether Sessions did so correctly today. Importantly, Sessions said Trump had not yet asserted executive privilege, and he himself had no power to claim it.
But Sessions said he did not want to reveal details that the President might want out of the public eye, if he were given more time to consider.
"It's my judgment that it would be inappropriate for me to answer and reveal private conversations with the president when he has not had a full opportunity to review the questions and to make a decision on whether or not to approve such an answer," Sessions said.
Scott Fredericksen, a former federal prosecutor and associate independent counsel now in private practice at Foley & Lardner, said Sessions had taken a "legitimate position . . . to protect the confidentiality of his conversations with the President."
"I think there's fairly good history that the Department of Justice resists revealing internal deliberations and discussions, whether it be investigations or policy, as a matter of separation of the executive from the legislative branch," he said.
But Cornell Law School professor Jens David Ohlin said Sessions' reasoning did not make sense.
"His justification for refusing to answer the questions was completely incoherent. He claimed executive privilege but then denied that he had done so," Ohlin said. "It made no sense whatsoever. He's basically trying to have his cake and eat it, too: claim executive privilege but then pretend that he didn't. His position has no basis in law, common sense, or logic."
Sessions declined to detail his conversations with the President on a number of topics - including the firing of FBI Director James Comey and possible discussions of pardons or the Russia investigation. He did, though, offer some specifics on why Comey was fired - a point King said showed he was being choosy in what he was willing to discuss.
Legal analysts agreed it was the President who would have to invoke privilege - although Fredericksen said Congress would have to push the issue if the members really wanted answers. Ultimately, Fredericksen said, a court might determine whether the information is public or not, but all involved would probably want to avoid that outcome.