(CNN) After a weekend of confrontation, sporadic violence and arrests during protests against the police shootings of black men, the mother of one of the victims has appealed for calm.

Valerie Castile, mother of Philando Castile, one of two African American men killed by police last week in separate shootings, sent a statement to media via her attorney Sunday.

"We urge all people to remain peaceful in all demonstrations throughout our community and our nation," the statement read.

"When demonstrations become violent, it disrespects my son and his memory. Philando was a man of peace and dignity.

"I ask you to at all times remain peaceful in your expressions of concern regarding his death at the hands of the police. I promise that we will not rest until justice prevails."

The call for calm came another night of intense, sometimes violent protests.

At least 309 people have been arrested over the weekend in New York and Chicago, and in St. Paul, Minnesota, and Baton Rouge, Louisiana, where two black men, Philando Castile and Alton Sterling, were shot to death by police. The killings have sparked several days of protests.

Dallas cop-killer had 'other plans'

The same week Sterling and Castile were killed, a gunman killed five police officers at a Black Lives Matter rally in Dallas.

Their killer was an Afghanistan war veteran, 25-year-old Micah Xavier Johnson from the Dallas suburb of Mesquite, Texas.

Johnson was plotting larger attacks, Dallas Police Chief David Brown said in an interview with CNN's Jake Tapper on "State of the Union" Sunday.

He said police found bomb-making materials and a journal at the shooter's home that suggested he'd been practicing detonations and appeared ready to take aim at larger targets.

Three other shootings, in Tennessee, Missouri and Georgia, have endangered police during rallies.

Prominent activist arrested

Black Lives Matter activist DeRay Mckesson, a public school administrator who is considered among the movement's loudest voices, was among 125 people arrested Saturday night in Baton Rouge, where Alton Sterling was shot and killed last week. Another 124 protesters were arrested.

Baton Rouge Police Chief Carl Dabadie Jr., at a press conference Sunday to explain the arrests, acknowledged a Baton Rouge officer pointed an assault weapon at protesters, but he said a supervisor immediately intervened to secure the weapon from her.

"That is being addressed by us also," Dabadie said. "My officers are human. They are tired. They are scared."

Louisiana Gov. John Bel Edwards, who called the press conference, said most protests had been peaceful -- with most arrests for minor offenses -- and blamed outside agitators for incitements to violence.

"That will not be tolerated -- we don't operate like that in Louisiana," Edwards said. "The best way to honor the memory of Alton Sterling, the Dallas officers and Philando Castile, is through peaceful protest.

"It is critically important that you follow the directions of law enforcement."

Sunday protests

More marches took place around the nation Sunday. In Boston, organizers announced on Facebook: "This is a peaceful protest. Please keep violence at home."

In Washington, on the fourth night of protests, several hundred protesters who had marched two miles to Union Station accepted without complaint the news from organizers and police that they could not march on the Capitol without a permit.

At the rally, the Rev. Matthew Watley, of Reid Temple AME Church, said people are looking for healing after having old wounds of racism reopened by the events last week.

He also said he wants the community to work with law enforcement.

"We don't want to be profiled as African-Americans, we also can't profile law enforcement because the supermajority of them are trying to do the right thing," he said.

Problems at protests earlier in the weekend

102 protesters were arrested. They were demonstrating against the In St. Paul, about102 protesters were arrested. They were demonstrating against the killing of Philando Castile , a school nutrition services supervisor. Last week, Castile was driving a car and was with his girlfriend, Diamond Reynolds, when they were pulled over for a broken taillight.

Reynolds posted a Facebook video of the aftermath of Castile's shooting. Castile told the officer he was armed and had a concealed carry permit, she said. The officer asked him for his license and registration and as he went to retrieve those items, the officer shot him multiple times, she explains as the recording continues.

The killings have saddened and angered Americans of all racial backgrounds, and spurred thousands to march. There have been mostly peaceful demonstrations, including in Chicago, where three were arrested Saturday. Throngs protested in New York, where 20 people were arrested.

Demonstrations have unfolded in cities including Washington, Atlanta, Miami and Fort Lauderdale, Florida.

In Atlanta, a group of protesters on Friday confronted police over Interstates 75 and 85, then moved into the Midtown business district. A smaller protest was held Saturday. Eleven were arrested.

Marchers also took to the streets Saturday night in Miami, with police saying Interstate 395 was briefly shut down. A reporter for CNN affiliate WPLG tweeted that demonstrators had blocked a major thoroughfare.

#BlackLivesMatter demonstrators have blocked Biscayne Blvd at NE 5th St. Traffic is not moving. @WPLGLocal10 pic.twitter.com/IJtwSOjdWZ — Liane Morejon (@LianeMorejonTV) July 10, 2016

In Fort Lauderdale, a large group of Black Lives Matter supporters walked to the Broward County Courthouse and then the county jail, where prisoners heard their shouts and tapped on windows in response, WPLG reported

Rocks, bottles fly in St. Paul

In St. Paul, however, scuffles broke out between protesters and police on Interstate 94.

JUST WATCHED Protesters shut down highway Replay More Videos ... MUST WATCH Protesters shut down highway 00:47

Demonstrators blocked the freeway, and threw bottles, bricks and fireworks at police, authorities said.

At least five officers were injured by protesters -- one hit with a glass bottle and another by fireworks, according to St. Paul police. One was hit on the head with a large piece of concrete, possibly dropped from a bridge, according to police.

Police say a Molotov cocktail was thrown at officers.

As many as 200 people forced their way past Minnesota State Patrol troopers who were trying to block them from getting on the road. Approximately 50 of the 102 people arrested were collared at the freeway.

JUST WATCHED Black families: We worry every day Replay More Videos ... MUST WATCH Black families: We worry every day 01:29

Black Lives Matter crosses the Atlantic

Hundreds of demonstrators took to the street in London Sunday to show support for the Black Lives Matter movement. Kicking off from Oxford Circus, London, where crowds marched toward the U.S. Embassy chanting "No justice, no peace" and "Hands up. Don't shoot!" Some roads were brought to a standstill.

London resident Aifur Rahman, who described himself on social media as a mathematics graduate, said the event was astonishing in its protest against police shootings in the United States.

Demonstrators sit in the road on Parliament Square in central London on Sunda.

"It brought many communities together and gave everyone a sense of unity in the fight against oppression and racial inequality," he said.

One man in attendance, named Banditsu, told CNN: "Black lives matter, I'm tired of seeing my brothers and sisters becoming a hashtag. Every day I wake up another black person is dead, that's why I'm here today. "

JUST WATCHED Cops' families: We worry every day Replay More Videos ... MUST WATCH Cops' families: We worry every day 01:28

#DCprotest: After #PhilandoCastile's death, this couple says they worry about bringing a son into this world pic.twitter.com/UzswV4cBX2 — Sherisse Pham (@Sherisse) July 9, 2016

Black Lives Matter protesters condemned the Dallas killings , calling the attack on law enforcement a tragedy not just for those affected but also for the nation.

"Black activists have raised the call for an end to violence, not an escalation of it. (Thursday's) attack was the result of the actions of a lone gunman," the group said.

"To assign the actions of one person to an entire movement is dangerous and irresponsible. We continue our efforts to bring about a better world for all of us."