Protesters defied curfews across the United States on Tuesday as leaders scrambled to stem anger over police racism while President Donald Trump rejected criticism of his use of force to stop a peaceful rally. Standoffs between police and demonstrators angered by the death of George Floyd, an unarmed African-American man whose killing has brought once-in-a-generation protests to the nation for the past week, stretched into the night in cities from New York to Los Angeles. But there were fewer reports of the looting and violence that had soured street demonstrations in previous nights. Tens of thousands gathered earlier in Houston to pay a hometown tribute to Floyd, who grew up in the Texas city and is to be buried there next week. "Today is ... about George Floyd's family – we want them to know that George did not die in vain," Mayor Sylvester Turner told an estimated 60,000 people. A tearful Roxie Washington, the mother of Floyd's six-year-old daughter, said she wanted justice for him. "No matter what anybody thinks, he was good," she told a news conference. In New York, which on Tuesday prolonged its first curfew since the Second World War for the full week, reporters watched as hundreds refused to go home after the 8pm deadline, instead chanting slogans and peacefully walking the streets in Manhattan and Brooklyn. Protesters attempting to cross the Manhattan bridge were pinned there for an extended period by police on both sides, but were finally allowed to return to Brooklyn, according to a <em>New York Times</em> reporter on the scene. Mayor Bill de Blasio told CNN it had been "much calmer" a day after several Manhattan luxury stores were looted, praising an increased and "vast presence" of police on the streets. Minnesota took one of the first concrete actions to address the grievances behind the uprising, which began after Floyd's death on May 25 in the state's largest city, Minneapolis. The state launched a civil rights investigation of the Minneapolis Police Department, looking at possible "systemic discriminatory practices" going back 10 years, Governor Tim Walz tweeted. Former president George W Bush called on the US to examine its "tragic failures" and to "listen to the voices of so many who are hurting and grieving". And in Los Angeles, one of dozens of cities hit by unrest, police officers and Mayor Eric Garcetti dropped to their knees in a symbolic act of solidarity as they met marchers led by African-American Christian groups. "A black face should not be a sentence to die, nor to be homeless, nor to be sick, nor to be underemployed, nor to be under-educated," Mr Garcetti told them, inviting the leaders into City Hall for a discussion about the issues. But protesters gathered outside Mr Garcetti's residence late into the evening. An AFP reporter witnessed a group of at least 200 refusing to disperse and subsequently arrested. In Washington DC, thousands returned to the streets on Tuesday for a peaceful Black Lives Matter march. Hours after the 7pm curfew protesters could be heard chanting, as National Guard troops stood on the streets near the White House and helicopters hovered above. Broadcast footage showed police using tear gas shortly after midnight, but the situation appeared to be calm overall. "I'm just tired, essentially, of being scared of police, of not getting justice," said Jada Wallace, an 18-year-old protester outside the White House earlier who said she was ready to risk arrest. In the same place on Monday, federal police had abruptly used tear gas and fired rubber bullets to beat a non-violent protest, clearing a path for Mr Trump to stroll outside for a photo opportunity at a historic church damaged the previous night. The move was condemned by religious leaders, the president's political rivals, and onlookers around the country. But Mr Trump, who has rejected the traditional presidential role of healer, voiced glee on Twitter over the response in Washington and accused the leadership of New York – led by the rival Democratic Party – of succumbing to "Lowlife & Scum". "Overwhelming force. Domination," he wrote, adding: "Washington, DC, was the safest place on earth last night!" He lashed at the critics later on Twitter, writing: "You got it wrong! If the protesters were so peaceful, why did they light the Church on fire the night before? People liked my walk." Joe Biden, Mr Trump's presumptive Democratic rival in November elections, denounced the crackdown as an abuse of power and promised, if elected, to tackle the "systemic racism". "Donald Trump has turned this country into a battlefield driven by old resentments and fresh fears," Mr Biden said in Philadelphia, also hit by violence. The United States also faced unusual, if polite, criticism from some international allies including Germany, the UK and Australia. German Foreign Minister Heiko Maas called the anti-racism protests "understandable and more than legitimate". "I hope that these peaceful protests won't slide further into violence, but even more than that I hope that they will make a difference in the United States," Mr Maas told reporters. A Las Vegas officer was in "grave condition" on Tuesday after being shot during protests overnight. An armed Hispanic man was shot and killed by police after raising his gun in a separate, nearby incident. Four officers were also shot overnight in St Louis. None of the injuries were life-threatening. But one retired St Louis police captain was shot dead early on Tuesday outside a ransacked store. Mr Trump tweeted that David Dorn, who was black, was "viciously shot and killed by despicable looters".