There remains a challenge, though, in the GOP-led chamber to pass the George Floyd Justice in Policing Act of 2020, which was approved by a 236-181 vote in the House in June. Of note, three House GOP members voted for the bill that largely passed along party lines.
Three Democratic lawmakers - U.S. Reps. Sheila Jackson Lee, Al Green and Steven Horsford, of Nevada - addressed with reporters Tuesday their effort to press Senate colleagues to pass the bill.
The legislation, which is aimed largely at ending racial profiling among police departments, would ban chokeholds and no-knock warrants in drug cases and reform qualified immunity, making it easier to pursue claims against police officers in civil court.
Other requirements in the House bill include incentives for state attorneys general to investigate local police departments, and providing grants for states to create procedures for investigating police-involved deaths.
SEE MORE: 'Stop the pain,' a brother of George Floyd tells Congress
The legislation seeks to improve transparency by creating a National Police Misconduct Registry, and mandate state and local law enforcement turn over data on use of force broken out by race, gender, disability, religion and age.
The bill also aims to address cultural biases in police stations by mandating racial bias training. It would change the standard for evaluating whether use of force was justified. Currently, officers only need to prove that use of force was "reasonable." The House bill would change the standard so that officers need to prove that use of force is "necessary."
The measure would require federal law enforcement officers wear body cameras.
Lawmakers acted within weeks after the death of native Houstonian Floyd, whose neck was pinned to the ground underneath a Minneapolis police officer's knee. The incident went viral after it was recorded by bystanders.
SEE ALSO: Congressional bill for police reform bears George Floyd's name
Senate Republicans offered a counter to the George Floyd Act with the Justice Act, which was touted as the party's most ambitious policing proposal in years. While the GOP bill offered federal incentives to compel change, Democrats rejected it, adding that it didn't go far enough to address questionable use of force practices.
The bill may ultimately be dead on arrival when the Senate returns from summer recess this month. Senate Majority Leader Mitch McConnell made it clear that he has no intention of bringing the House bill to the floor of the Senate for a vote without changes.
Meanwhile, the Congressional briefing with reporters is coming a day after five Houston city council members expressed "no confidence" in Mayor Sylvester Turner's independent citizen oversight board. Turner vowed that reforms are coming to Houston police.
ABC News contributed to this report.