Mr Trump spoke to governors on a video teleconference with law enforcement and national security officials in the aftermath of another night of violent protests in dozens of US cities.
The US President told local leaders they “have to get much tougher” after six days of unrest set off by the death of George Floyd, a black man who died after he was pinned at the neck by a white Minneapolis police officer.
“Most of you are weak,” Mr Trump told governors, telling them to "arrest people.”
Meanwhile, Mr Floyd's brother Terrance urged protesters to "do this another way" as he appealed for calm.
ITV News Washington Correspondent Robert Moore explains 'how Washington D.C has not seen an atmosphere like this since 1968'
Speaking at a makeshift memorial for his brother, Mr Floyd said: "I understand y'all upset like it was already said, I doubt y'all are half as upset as I am. So if I'm not over here wilding out, if I'm not over here blowing up stuff, if I'm not over here messing up my community, then what are y'all doing?"
"What you are doing, y'all not doing nothing, because that's not gonna bring my brother back at all."
Terrence Floyd dropped to his knees when walking up to the memorial and prayed as chants of "George Floyd" from the crowd rang out.
He called on protestors to find another way to vent their outrage at his brother's death.
"In every case of police brutality, the same thing has been happening. Y'all, protest, you destroy stuff. And they don't move, you know why they don't move? Because it's not their stuff, it's our stuff. So they want us to destroy our stuff. They not going to move. So let's do this another way. Let's do this another way."
Protestor, Arianna Evans, told ITV News, "American people are tired of being oppressed" and if President Donald Trump does not listen to the US people, they "will vote him out in November."
"We are tired of being oppressed, we are tired of being hurt, black people are tired of dying in the street for no reason," she said.
"Hear our voices, sit down with us, meet us at the table and meet our demands."
While many of the demonstrations around the country have been peaceful protests by racially diverse crowds, others have descended into violence, despite curfews in many cities and the deployment of thousands of National Guard troops in at least 15 states.
They turned violent in several cities, with looting and mayhem, and fires ignited in the historic park across from the White House.
ITV News Washington Correspondent Robert Moore encountered activists pleading with the police to show restraint with some protestors kneeling in front of the police lines.
During a protest in Washington DC, Mr Trump as hundreds of people protesting against the death of Mr Floyd gathered outside the executive mansion, some of them throwing rocks and tugging at police barricades.
Mr Trump spent nearly an hour in the bunker, which was designed for use in emergencies like terrorist attacks, according to a Republican close to the White House who was not authorised to publicly discuss it and spoke on condition of anonymity.
“The White House does not comment on security protocols and decisions,” said White House spokesman Judd Deere, while the Secret Service said it does not discuss the means and methods of its protective operations.
The president and his family have been shaken by the size and venom of the crowds, according to the Republican source.
It was not immediately clear if First Lady Melania Trump and the couple’s 14-year-old son, Barron, joined the president in the bunker, though Secret Service protocol would have called for all those under the agency’s protection to be in the underground shelter.
Mr Trump travelled to Florida on Saturday to view the first manned space launch from the US in nearly a decade.
He returned to a White House under virtual siege, with protesters, some violent, gathered just a few hundred yards away through much of the night.
Demonstrators returned Sunday afternoon and on Monday, facing off against police at Lafayette Park into the evening.
As cities burned night after night and images of violence dominated television coverage, Mr Trump’s advisers discussed the prospect of an Oval Office address in an attempt to ease tensions.
But the notion was quickly scrapped for lack of policy proposals and the president’s own seeming disinterest in delivering a message of unity.
In recent days security at the White House has been reinforced by the National Guard and additional personnel from the Secret Service and the US Park Police.
On Sunday, the Justice Department deployed members of the US Marshals Service and agents from the Drug Enforcement Administration to supplement National Guard troops outside the White House, according to a senior Justice Department official who spoke anonymously.