(CNN) President Donald Trump's examination on race is not over, not by a long shot.

Trump finally bent to intense pressure and called out white supremacist groups on Monday, as the fallout from rallies in Charlottesville, Virginia, that led to a woman's death rocked his administration.

But the real Donald Trump is not typically revealed in the Diplomatic Room of the White House, where he made a formal, scripted statement that attempted to manufacture the political space required to move on from the controversy.

Given that Trump's natural habitat is on Twitter or in ad-libbed sparring with reporters, the true measure of his sincerity over Charlottesville will come only when the next racial uproar erupts and the President fires off his heat-of-the-moment response. That instinct was on display Monday evening, when he retweeted a far-right conspiracy theorist, Jack Posobiec, who asked why there was "no national media outrage" following a spate of deadly shootings in Chicago over the weekend.

That instinctive reflex was what got him into trouble Saturday, when he condemned violence on "many sides," appearing to draw a moral equivalence between neo-Nazis and opponents who showed up to protest their rally.

It took two days for Trump to concede he needed to clean things up, as it became clear the episode was not just the latest lurching twist in a reality-defying political era, but had real potential to seriously damage his presidency.

In a sign that that the President's comments had failed to quell the controversy, the CEOs of Intel and Under Armour announced Monday night they would follow Merck CEO Kenneth Frazier in quitting Trump's manufacturing council.

He won some plaudits, especially from his own party, for the robust, uncompromising tone of his Monday statement in which he declared: "racism is evil."

"Those who cause violence in its name are criminals and thugs, including the KKK, neo-Nazis, white supremacists, and other hate groups that are repugnant to everything we hold dear as Americans," Trump said.

Oklahoma Republican Sen. James Lankford said the President was "clearly communicating the evilness of racism."

South Carolina Sen. Lindsey Graham tweeted: "Well done Mr. President."

Many Washington politicians and pundits conceded that it was important Trump had said what he said. Yet there was still some disquiet that it took him so long to take a such a clear stand.

"Today, the President's remarks were clear and specific. However, they would have been more impactful on Sunday," said Sen. Tim Scott, the only black Republican in the Senate, tweeted. "I hope this serves as a lesson for all that when a community grieves, when Americans look for guidance after such a crushing and devastating attack like the one that unraveled this weekend in Charlottesville, we must take a firm stance against hate and violence."

Trump will likely have to do more to convince skeptics he was speaking from the heart -- partly because his social media posts have often been a more faithful representation of his inner thoughts than his official statements.

"Made additional remarks on Charlottesville and realize once again that the #Fake News Media will never be satisfied...truly bad people!" Trump tweeted Monday afternoon.

Made additional remarks on Charlottesville and realize once again that the #Fake News Media will never be satisfied...truly bad people! — Donald J. Trump (@realDonaldTrump) August 14, 2017

'Stemmed some of the flow of blood'

Trump's initial response to the tragedy remains shocking three days later. After all, the United States was founded on the principle that all men are created equal, and it took the American President, the de-facto moral leader of the nation, two days to repudiate white supremacists by name.

Critics also faulted Trump for his somewhat grudging tone on Monday.

"I think we should acknowledge up front that the President did the right thing today, we have been pounding on him for two days in the media, in politics in newspapers, everywhere," said David Gergen, an adviser to Republican and Democratic presidents, on CNN's "Erin Burnett OutFront." "Having said that, I think he has stemmed some of the flow of blood, but he is grievously wounded over this."

If Gergen is right, it will take far more than Monday's speech, read from a teleprompter, to restore the moral authority of this presidency.

The White House may recognize that, since Trump's appearance did represent a subtle shift in tactics.

During other recent kerfuffles, including his escalatory rhetoric on North Korea, the President relied on aides and subordinates to explain and reshape his remarks, including his secretaries of state and defense.

But that approach was no longer sustainable on this issue, a fact that Trump's appearance, on a brief trip home to the White House from his working vacation at his Bedminster, New Jersey, golf resort, seemed to acknowledge.

JUST WATCHED Trump's day-by-day response to Charlottesville Replay More Videos ... MUST WATCH Trump's day-by-day response to Charlottesville 01:49

Will Twitter get Trump in trouble again?

As so often happens, the President's own actions undermined his attempt to mitigate his own political problem. And, as often before, his tweets did the damage.

Early Monday, Trump was quick on the draw on the social media site, after Frazier, the CEO of Merck & Co, pulled out of his manufacturing council over the President's initial failure to condemn white extremists.

The blast begged the question of why he could condemn Frazier, a prominent African-American business leader, in real time, but took two days to call out extremists.

He also attacked Frazier after his speech, tweeting: "@Merck Pharma is a leader in higher & higher drug prices while at the same time taking jobs out of the U.S."

The sense that Trump was only grudgingly bowing to pressure Monday was bolstered by the way he chose to begin his speech. He boasted about the state of the economy, and highlighted his trade policy in a campaign-style riff.

Aides told CNN that it was Trump's choice to talk first about the soaring stock market, in remarks that raised questions about his priorities.

Trump's past is another reason why the events of the weekend will not simply blow over.

After all, Trump anchored his political rise on a racially motivated lie -- that Barack Obama, the first African-American president, was not a natural born American. He stumbled over repudiating David Duke, the former leader of the Klan, during an interview with CNN's Jake Tapper during the presidential campaign.

Some Trump critics believe that his linguistic contortions are a direct result of a desire to avoid alienating extremists who are sympathetic to his brand of economic nationalism and tough immigration policy while convincing other Americans he decries racism and bigotry.

"He wanted to have his hate cake and eat it," said Cornell William Brooks, former president of the NAACP, on "The Situation Room."

Though Brooks described the speech Monday as a "good first step," he warned it needs to be followed up by policy changes, calling on Trump to stop "signaling and engaging in messaging, racial dog whistles with the Alt-right."

"The fact of the matter is the whistles he blew during the campaign were answered in Charlottesville, and someone lost her life."