Bush related a conversation on race relations with former secretary of state Condoleezza Rice an African-American. "She just said you have to understand that there are a lot of black folks around that are incredibly more and more distrusting of law enforcement," he said.
Garner's mother, Gwen Carr, said she was "thrilled" by the protests. "It really warms my heart to see that people are out there," she said.
She angrily rejected Pantaleo's previous offer of an apology. "He wouldn't let him go. As my son begged for his life, he still held on," she said. "So it was like a thrill kill."
The officer's lawyer, Stuart London, said Pantaleo feared for his life as he grappled with the 159kg Garner in front of a plate-glass shopfront. He said the dead man had resisted arrest for allegedly selling untaxed loose cigarettes. The New York grand jury's decision not to prosecute came nine days after a similar panel in Ferguson, Missouri, decided not to charge a white officer for the fatal shooting of an unarmed black teenager.
In Cleveland, Ohio, protests erupted after the fatal shooting by another white policeman of a 12-year-old black boy who had been waving a toy gun.
In Phoenix, demonstrators marched on police headquarters after details emerged of the death this week of Rumain Brisbon, 34, outside a grocery store.
Police were called after witnesses told officers that the occupants of a car were selling drugs. One man seemed to grab an item from the back of the car and fled on foot with an officer in pursuit, police said.
There was a struggle and the officer fired two shots after he said he mistook what turned out to be a container of painkillers for a weapon. Police said a handgun and marijuana were later found in the vehicle.
The spate of police shootings and the two decisions not to indict the white officers have ignited nationwide outrage and calls for reform of the secret grand jury system and changes in how the law deals with minorities.
In cities across the country, demonstrators brought traffic to a standstill and staged "die-ins". In New York, about 200 people were arrested, mainly for minor offences, but the protests remained largely peaceful.
US attorney-general Eric Holder called for nationwide review of law-enforcement tactics. His department released a damning report about the Cleveland police department, condemning the use of excessive force, before the death of 12-year-old Tamir Rice as he played with a slug gun in a park.
New York mayor Bill de Blasio was condemned by police union leaders saying he wasn't supporting his officers as he outlined plans for retraining in dealing with the public.
President Barack Obama weighed in, saying one of the chief issues was "making sure that people have confidence that police and law enforcement and prosecutors are serving everybody equally". Talking about the Garner case, he previously said: "This is an American problem."
Caution surrounds royal visit
Kate and William.
Security will be stepped up around the Duke and Duchess of Cambridge, William and Kate, when they visit New York today.
Widespread demonstrations over the death of an unarmed black man at the hands of police came ahead of the royal couple's three-day tour of the US.
Yesterday it was claimed the couple will be given extra New York Police Department security in light of recent turmoil.
An NYPD spokesman declined to comment, but confirmed William and Kate "will be getting security".
Sources close to the couple, who will be joined by Scotland Yard bodyguards, said they will be subject to extra precautions.
"There is no suggestion of a direct threat but the way these demonstrations are spreading is being taken into account when planning their movement," said one.
William and Kate are due to arrive in New York this afternoon for a whirlwind trip, packing seven public engagements into two days.
Tonight they will attend a private dinner on behalf of American Friends of the Royal Foundation in New York.
William and his brother Harry set up the foundation in 2009.
Kate will remain in New York while William is in Washington.
