Several videos of police brutality have emerged during protests over the death of African American George Floyd.
In Buffalo two officers were suspended after they were seen shoving an elderly white man to the ground.
Meanwhile Indianapolis police are investigating the actions of officers after they were seen beating and firing pepper rounds at a black woman.
The reports come hours after a memorial for Floyd in Minneapolis, the city where he died at the hands of police.
His killing, also captured on video, has caused outrage and sparked a wave of protests against racial discrimination and police treatment of African Americans in cities across the US and the world.
The vast majority of demonstrations over the past eight days have been peaceful but some have descended into violence and rioting, with curfews imposed in a number of cities.
At one protest, security forces in Washington DC fired pepper balls and smoke bombs to disperse demonstrators outside the White House, allowing President Donald Trump to walk to a nearby church for a photo opportunity.
In response to this on Thursday, civil rights group the America Civil Liberties Union filed a lawsuit, accusing the president, the attorney general and others of violating the constitutional rights of protesters.
"When the nation's top law enforcement officer becomes complicit in the tactics of an autocrat, it chills protected speech for all of us," said ACLU official Scott Michelman, quoted by Reuters.
More on George Floyd's death
In a separate development, police in Arizona released details of the killing of another African American, Dion Johnson, in Phoenix on 25 May, the same day as Floyd.
Mr Johnson was shot dead by state troopers after being found "passed out in the driver's seat" of a car which was partially blocking traffic, a police statement said.
"During the trooper's contact with the suspect, there was a struggle and the trooper fired his service weapon striking the suspect," police said.
The statement was only released after Mr Johnson's family was offered audio of the police dispatch and transportation department video of the incident.
What do the videos show?
The Buffalo video shows a 75-year-old man approach police officers enforcing a curfew. They then move forward, pushing him back and causing him to fall over and hit his head.
As he lies on the ground, blood is seen pouring from his ear.
The man was taken away in an ambulance and was later found to have suffered a severe head injury.
An initial statement from Buffalo Police Department said the man had "tripped" and fallen during a "skirmish involving protesters", compounding outrage at the incident on social media.
Police spokesman Jeff Rinaldo later attributed the statement to officers not directly involved in the incident, adding that when the video had emerged the two policemen who pushed the demonstrator had been suspended without pay.
In Indianapolis, the Indianapolis Metropolitan Police Department is investigating after a video was widely shared on social media showing officers beating a woman with batons and shooting her with pepper rounds, the Indianapolis Star newspaper reported.
Different angle on 1️⃣1️⃣1️⃣ out of Indianapolis— T. Greg Doucette (@greg_doucette) June 4, 2020
From this view you can see the cop grope the woman he's restraining, that's why she breaks away
Then of course a half dozen cops beat her for not wanting to be groped
The footage, which has been viewed at least 8m times on Twitter, shows a white officer holding the woman with his arm near her chest. She then twists out of his grip and two other officers beat her with batons, dust clouds appear indicating that pepper rounds have been fired and an officer then presses her face against the pavement.
In Philadelphia a student who had been arrested on charges of breaking a police officer's hand has been released without charge after footage emerged of an officer beating him on the head with a baton and another pinning his face onto the street using his knee.
A biker gang brutally beat these protesters in Philly today. pic.twitter.com/r1TzXrOpNW— Morgan J. Freeman (@mjfree) June 5, 2020
The footage shows the 21-year-old student attempt to separate a police officer and a protester before then moving away when a police officer moves to strike him. The Philadelphia Inquirer said the officer had been removed from street duty pending an investigation.
In New York City a food delivery driver was arrested 27 minutes after the city's curfew had started, despite being a key worker exempt from the curfew.
NYPD officers arrest an essential worker—his Caviar bag is sitting by his bike, 27 min after curfew at 108 and Central Park West in Manhattan— peter hess (@PeterNHess) June 5, 2020
city and state officials assured essential workers they are exempt
at least three white shirts (commanding officers) are present pic.twitter.com/92aI7UdODU
And in the Williamsburg area of the city, police were filmed charging demonstrators, throwing at least one person to the ground.
Other videos showed a man lying on the ground bleeding from the head, and being arrested.
How have the authorities responded?
On Thursday New York State Governor Andrew Cuomo defended police, saying they were not beating citizens "for no reason", and if they did "it's wrong".
City Mayor Bill de Blasio said the authorities were "doing everything from a perspective of restraint".
But both men have since condemned the incidents which emerged overnight.
"Police officers must enforce - NOT ABUSE - the law," he said.
Meanwhile Mayor de Blasio said he had complained to the city police department after seeing the video of the arrest of the delivery worker.
What is the background?
The incidents happened as police enforced curfews in dozens of cities across the US after a wave of protests sparked by George Floyd's death.
Floyd, 46, was stopped by police investigating the purchase of cigarettes with counterfeit money on 25 May in Minneapolis.
A video showed him being arrested and a white police officer continuing to kneel on his neck for several minutes even after he pleaded that he could not breathe.
Protests erupted and have continued since, across many US cities and also internationally, with rallies on Wednesday in Australia, France, the Netherlands and in the UK, where thousands gathered in central London.
A rally in the Australian city of Sydney has been refused permission by a court, amid fears of coronavirus health risks. Thousands had been expected to attend.
Floyd's death follows the high-profile cases of Michael Brown in Ferguson, Missouri; Eric Garner in New York; and others that have driven the Black Lives Matter movement in recent years.
For many, the outrage over Floyd's death also reflects years of frustration over socio-economic inequality and discrimination.
Protests over the death continued in dozens of cities on Thursday despite widespread curfews.
They followed a memorial service attended by hundreds, who stood in silence for eight minutes and 46 seconds, the amount of time Floyd was alleged to have been on the ground under the control of police in Minneapolis.
A lawyer for George Floyd told the service a "pandemic of racism" had led to his death.
Giving the eulogy, civil rights activist the Reverend Al Sharpton said it was time to stand up and say "get your knee off our necks".