Washington (CNN) White House aides who steeled themselves for what President Donald Trump would say when he finally addressed the sexual assault allegation against his Supreme Court nominee Brett Kavanaugh were quietly stunned when Trump said the process should be followed and the accuser should be heard.

In recent days, Trump has bragged about the positive coverage he's received for his response, according to multiple sources. That response has contributed to him continuing to say Christine Blasey Ford should come forward with her story, they said.

As of Thursday, officials felt confident Kavanaugh was back on track toward confirmation.

Those who work closely with the fiery President knew he had privately voiced suspicion about the #MeToo movement , complaining that decades-old allegations could ruin men's lives in an instant. He himself stands accused of various levels of sexual misconduct by 15 women, all of which he has denied.

Behind the scenes

Multiple West Wing officials and outside advisers feverishly phoned Trump on Sunday in the wake of Ford's detailed account of the assault she says happened when she and Kavanaugh were teenagers. Kavanaugh has denied the allegation.

"Why would I attack her?" Trump asked, according to two sources with knowledge of his remarks.

Rather than lashing out in anger or defensiveness, Trump said Monday he'd like to "see a complete process."

"I'd like everybody to be very happy. Most importantly, I want the American people to be happy, because they're getting somebody that is great," he said.

Kellyanne Conway was the first White House official to appear on television after Ford came forward publicly. During an appearance on Fox News, Conway said Kavanaugh's accuser should testify.

"This woman should not be insulted and she should not be ignored," Conway said. "I think the Senate is headed to a reasonable approach in that it seems to be allowing this woman to be heard in sworn testimony, allowing Judge Kavanaugh to be heard in sworn testimony."

Conway said she had spoken with Trump and members of the Senate Judiciary Committee and that the White House agreed that the committee could work with Ford on how to testify.

"But remember, too, that has to be weighed against what we already know, which is that Judge Kavanaugh is a man of character and integrity," Conway added.

Encouragement

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Trump's more tactful approach earned him kudos from those around him, serving to reinforce his position.

Ivanka Trump has also highlighted the positive response the President has received for his measured reaction.

He has only referenced the Supreme Court once in Twitter this week — tweeting shortly before midnight Tuesday: "The Supreme Court is one of the main reasons I got elected President. I hope Republican Voters, and others, are watching, and studying, the Democrats Playbook."

Aides have noted that the President's measured response is partly because the allegation isn't against him.

During the 2016 campaign, at least 15 women accused Trump of misbehavior ranging from sexual harassment and sexual assault to lewd behavior around women. They came forward in the wake of a 2005 "Access Hollywood" tape that was released in October 2016 in which he is caught saying on a hot mic: "And when you're a star, they let you do it. You can do anything ... Grab them by the p****. You can do anything."

The White House -- through press secretary Sarah Sanders and others -- has dismissed all the allegations against him as old news that had been litigated during the campaign.

Trump is not personally close with Kavanaugh but enjoys touting his credentials. And though he has stood by Kavanaugh this week, he has told people close to him that Kavanaugh has to defend himself.

White House officials remain confident Kavanaugh will be confirmed.

After Ford's attorneys told CNN Tuesday night that she wanted an FBI investigation before testifying, officials felt they had regained the upper hand. One noted that if she doesn't testify, this will only be a blip on the radar of his legacy on the Supreme Court.