The ongoing protests in Portland have been escalating due to backlash against the use of federal agents, which Trump has suggested sending to multiple cities across the US.
The program involves deploying federal law enforcement agents to assist local police.
Democrats said they hoped the legislation would win bipartisan support.
Philadelphia Mayor Jim Kenney predicted the deployment of federal agents would backfire by exacerbating tensions at a time when the cities are still grappling with the spread of COVID-19.
The incident, caught on video by bystanders, sparked massive and continuing protests against racial injustice and calls for police reforms.
Accusations have been circulating claiming that the tactics the US police used to kill George Floyd were learned from the Israeli police.
"I wanted to ask them 'Why are you guys not following the Constitution?' But we never got there," David said in an interview. "They whaled on me like a punching bag."
Portland has been the site of protests against racial inequality and police brutality for the past 50 nights, in the wake of the death of George Floyd at the hands of police officers in Minneapolis o
These shifts have been especially notable on Twitter, where the typical member of Congress tweets nearly as twice today compared with a similar time period in 2016.
The lawsuit was filed at US District Court in Minneapolis by Ben Crump, a civil rights attorney who has represented other families in high-profile police killings of Black men.