But in a statement on a crowdfunding page for Harry’s cause, spokesman Radd Seiger castigated the White House for attempting to spring a surprise meeting between the Dunns and Sacoolas in front of the press.

“The family had four surprises yesterday,” Seiger said in the statement, calling the initial invitation to the White House “out of the blue” and adding that the family had no idea Trump would meet with them personally. But, he continued, they were unaware that Sacoolas would even be in the building.

“It was the President’s intention for Harry’s family to meet Mrs Sacoolas in the Oval Office in front of several photographers in what [was] obviously designed to be a press call,” Seiger said.

The Dunns declined the meeting with Sacoolas. Seiger went on to reiterate that while the Dunn family wished to see a political and diplomatic solution to their dispute, “and need one to happen quickly for the sake of their health,” they hope to meet with Sacoolas “one day in the future but in a neutral and appropriately controlled environment.”

In an interview on “CBS This Morning” on Wednesday, the Dunns admitted to feeling “a bit [of] pressure” from Trump, noting that "he did ask two or three times” but “we stuck to our guns."

Seiger ripped the White House — singling out new national security adviser Robert O’Brien in particular — for the ham-fisted attempt at mediation.

“It struck us that this meeting was hastily arranged by nincompoops on the run and in particular Mr O’Brien who appeared to be extremely uptight and aggressive and did not come across at all well in this meeting which required careful handling and sensitivity,” he said.

While the Dunns said that they were shocked at the offer, they also expressed compassion for how Sacoolas was handling the situation.

"To be thrown into a room together with no prior warning, that's not good for her mental health, it's certainly not good for ours. You know, none of us know how we were going to react to have that sprung on us," Charlotte Charles said.

Seiger did praise Trump’s attention to the issue, saying that Trump offered his condolences to the Dunns, and that they were “warmly received.” And he added that it appeared Charlotte Dunn’s emotional appeal had prompted Trump to reconsider his approach to solving their “nightmare scenario.”

On CBS, Charlotte Charles detailed her interaction with the president.

“At the end of the meeting, we all shook hands, and I ended up at the back of our little family queue and President Trump actually grabbed hold of my hand. So I squeezed it tight, and I just said to him, 'Please, you know, just do the right thing. You know, if you had a son, you'd be doing the same. You've said that,'” she said. Trump responded in the affirmative, telling her “I absolutely would,” she added.

Trump has publicly remained ambivalent on the situation. Last week, he said he was “trying to work something out” regarding Sacoolas, and he’s personally been lobbied by British Prime Minister Boris Johnson over the issue. At a White House event last week the president told reporters he was confident both sides could reach a solution.

Still, he called the case “complex” and told reporters that he hated the conundrum. He added that he would speak to Sacoolas herself and “see what we can come up with so that there can be some healing. There’s tremendous anger over it. It’s a terrible incident. There’s tremendous anger, and I understand the anger from the other side very much.”

Speaking to reporters Wednesday, Trump did not comment on the Dunns' reaction to the meeting, but described it as "beautiful in a certain way."

The president appeared to suggest that his British counterpart asked him to set the meeting up, but Trump said that when he offered to bring Sacoolas into the room, "They weren't ready for it."

"They did not want to meet with the person in question, but we had a very good meeting," he said, adding that "it was very sad, to be honest. They lost their son."

At the same time, as he has before when discussing the Dunns' case, Trump appeared to deflect some blame from Sacoolas, arguing that Americans driving in the U.K. are prone to confusion over reversed traffic lanes.

"You go to Europe and the roads are opposite. It's very tough if you are from the United States," he said. "The roads are opposite. She said that's what happened. It happens to a lot of people, by the way."

Asked whether he'd known if the Dunns had expressed interest in meeting Sacoolas, Trump replied that he'd guessed so. "I thought they were, based on what I saw they wanted to meet. but now they say only want to meet if they were in the U.K.," he said.

In a statement, White House press secretary Stephanie Grisham confirmed that Tuesday's meeting was arranged at the request of the British prime minister, adding that Trump's "intent was to do all he could to comfort the victims of a tragic accident."

An attorney for Sacoolas told CBS News her client, too, was unaware she would potentially be meeting the Dunns when she was invited to the White House on Tuesday.