Americans "cannot let the actions of a few define all of us," US President Barack Obama said Saturday, calling on Americans grieving from three consecutive shootings this week to stand together and unite against acts of violence.

The US has been reeling from a week of gun-fueled violence that saw two black men fatally shot by police on Tuesday and Wednesday, followed by a mass shooting that targeted police officers at a peaceful rally protesting violence against the black community.

"This has been a tough week, first and foremost for the family of those killed, but also for the entire American family," Obama said at the start of a press conference during a NATO summit in Warsaw.

"As painful as this week has been, I firmly believe that America is not as divided as some have suggested," Obama said.

A wave of nationwide grief began on Tuesday, when Alton Sterling, 37, was tackled and shot by police after selling CDs outside a convenience store in Baton Rouge, Louisiana.

The next day, Philando Castile, 32, was fatally shot at a routine traffic stop in suburban Minneapolis, Minnesota. Castile's fiancee recorded the aftermath using Facebook Live as her boyfriend bled profusely while the officer continued pointing his firearm at him.

On Thursday, as demonstrators in Dallas, Texas, came together to mourn Sterling and Castile and show solidarity for the Black Lives Matter movement, a US military veteran opened fire on police who were guarding the march, killing five officers, wounding seven officers and two civilian bystanders.

Police identified the lone gunman as Micah Xavier Johnson, 25, a black military veteran who told officers he was angry about the killing of black men by police officers and wanted to kill police.

Police said they killed Johnson with a bomb carried by a robot into the parking garage where the assailant had taken cover. A search of Johnson's home turned up bomb-making materials, ballistic vests, rifles, ammunition and a personal journal of combat tactics.

Obama described the gunman as "demented" and went on to say that, though Americans felt sorrow, anger and confusion over the shootings, they could unite against the incidents and reject them as part of their collective identity.

"This is not who we want to be as Americans, and that serves as the basis for us wanting to move forward in a constructive and positive way," Obama said.

The US president will make an abbreviated stop in Spain on Sunday before returning to the United States to address issues surrounding the attack and visit Dallas next week. He will meet with King Felipe VI and Prime Minister Mariano Rajoy in Madrid, marking the first visit by a US president to Spain in 15 years.

A stop in Sevilla and a meeting with young people in Madrid were canceled so that Obama can travel home and prepare for his visit to Dallas.

Protests continued late Friday in US cities as people demanded justice for the African American victims of police violence.

Obama said Americans of all backgrounds were outraged about the deaths of the two black men and said he wanted to "start moving on constructive actions that will actually make a difference" in improving race relations in the US.

He said there was not "enormous polarization" in the US and it had not reverted to the situation that existed in the '60s when rioting over segregation tore at the fabric of numerous US cities, resulting in numerous deaths and mass destruction.

Police nevertheless have increased security in cities across the country amid fears of copy-cat attacks.

Thousands of Black Lives Matter marchers disrupted traffic in Atlanta on Friday and demonstrators also descended on New York's Times Square and the Justice Department in Washington. In New Orleans, protesters lay down in a "die in" in front of police headquarters, the Times-Picayune newspaper reported.

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