Thousands have protested across the US over police killings of black men for a fifth straight day, with several people - including a prominent activist - arrested for violence and disruption.

Demonstrations continued into the early hours of Sunday, as what US President Barack Obama has called a "very tough week" drew to a close, five days after Alton Sterling - a 37-year-old black man and father of five - was killed by white police in Baton Rouge, Louisiana.

His death was followed by the police killing in Minnesota of Philando Castile, a young black man who worked at a local school serving food to children. Castile's death was filmed by his girlfriend, Diamond Reynolds, and streamed live on Facebook.

On Thursday, five white police officers were killed by a suspect named as Micah Johnson, a former US soldier who police said claimed he wanted to kill white people.

Obama said Americans of all races and backgrounds were "rightly outraged" by the attack in Dallas, and "rightly saddened and angered" by the fatal police shooting of both Sterling and Castile. 

Seeking to calm tensions, he said America was not "as divided as some suggest".

'I'm under arrest, y'all'

On Saturday night, as a few hundred protesters gathered at the Baton Rouge Police Department, police arrested DeRay Mckesson, a key figure in the Black Lives Matter movement.

Mckesson streamed his own arrest live on Periscope, and could be heard saying, "I'm under arrest, y'all" as fellow protesters asked why he was being held.

The protest seemed tense as police in riot gear appeared on the scene, apparently to clear the road so traffic could pass. A police spokesman said two firearms were confiscated and several arrests made, the Associated Press news agency reported.

Protesters waved homemade signs while drivers honked their horns in support and some stopped with bottles of water.

In Minnesota, police said arrests were made after protesters began throwing fireworks, bottles and rocks at officers during a protest that shut down a section of Interstate 94, a motorway, on Saturday night.

The march started outside the governor's mansion, where protesters have gathered since Castile's death. 

About 100 protesters remained just before midnight as police, some in riot gear, walked toward them. The St Paul Police Department tweeted that multiple officers were injured by fireworks thrown by protesters. It wasn't immediately clear how many people had been arrested.

Other rallies were held in California, Colorado, Florida, New York, Pennsylvania, Rhode Island and Utah. Hundreds gathered in each city, with up to 1,000 people joining the march in New York.

A protester is loaded into a NYPD police car after being arrested in Manhatten [Bria Webb/Reuters]

Source: Al Jazeera and agencies