New York (CNN Business) American reporters asked President Trump about Michael Cohen's testimony during a photo opportunity between Trump and North Korean dictator Kim Jong Un on Wednesday.

Trump didn't answer. Less than an hour later, the White House blocked several reporters from attending the next media availability between Trump and Kim.

Press secretary Sarah Sanders cited "the sensitive nature of the meetings."

But the press limitations were an abrupt change -- suggesting that the president didn't want to hear any more questions about Cohen.

The result: Fewer eyewitnesses were present at the start of Trump and Kim's controversial meeting in Hanoi, Vietnam.

The White House Correspondents Association criticized the administration's "capricious decision" to retreat behind "arbitrary last-minute restrictions on coverage."

"We call on the White House to not allow a diminution of the previously agreed-to press complement for the remainder of the summit," the association said.

The episode came two days after the international media was forced to move out of a hotel in Hanoi because, it turned out, Kim was also staying there.

TV networks and other news outlets had to relocate -- prompting grumbling from reporters who said that the White House should have stood up for the American press.

Past administrations have pointedly advocated for press access during meetings with repressive governments. The idea was to demonstrate what American democracy looks and sounds like -- pesky reporters and all. But several White House correspondents said the Trump administration is behaving differently.

"A lot of catering to Kim Jong Un going on in Vietnam," CNN's Jim Acosta tweeted. "First press is kicked out of hotel where Kim is staying. Now some reporters are blocked from pool spray because the dictator doesn't like shouted questions."

"Pool sprays" are when a representative group of journalists are allowed to witness a presidential event. Normally they also shout some questions when they see an opening to do so. This custom has existed for decades.

Reporters from the Associated Press and Reuters asked about Cohen and North Korean denuclearization during Wednesday's first "pool spray" with Trump and Kim.

Staffers from North Korea's government-controlled media were also in the room, but they don't have the same freedom to shout questions.

American reporters were anticipating the same level of access for the evening's next photo op, during dinner, but then "Sanders informed us that no print reporters would be allowed in due to sensitivities over shouted questions in the previous sprays," according to Vivian Salama of the Wall Street Journal. Salama was Wednesday's assigned "print pooler," one of many people who serves in a rotation.

So in other words, according to Salama, the White House was okay with photographers and camera crews being present -- to take pictures -- but not with the AP and Reuters reporters being there. Correspondents from the Los Angeles Times and Bloomberg were also blocked.

Thanks to a show of press solidarity, the White House opened up access a little bit.

"When our photo colleagues joined us in protest, they decided to allow one print reporter in," Salama wrote.

So Salama was in the room to witness Trump and Kim's Wednesday night dinner. The other reporters were not.

According to Salama's recap, Trump asked the small group of journalists if they were all "having a good time."

He pointed to photographer Doug Mills of The New York Times and told Kim that Mills is "one of the great photographers of the world."

Sanders said in a statement that the White House "ensured that representation of photographers, tv, radio and print Poolers are all in the room."

"We are continuing to negotiate aspects of this historic summit and will always work to make sure the U.S. media has as much access as possible," she added.

A similar dispute happened during Trump and Kim's first summit in Singapore last year.

Acosta was excluded "from the first couple of pool sprays," he said on CNN, "and the reason I was given is they were concerned that Kim Jong Un had not been around American reporters yelling questions, shouting questions and so on."

After Wednesday's episode, The Associated Press issued a statement that sharply criticized the Trump administration.

"The AP decries such efforts by the White House to restrict access to the president," the news service said. "It is critically important that any president uphold American press freedom standards, not only at home but especially while abroad."

Reuters also issued a statement saying that the news outfit was "deeply troubled" by the restriction: "We believe it is essential that government provide access to -- and the ability to ask questions of -- officials and hold them to account."