(CNN)House Majority Leader Steny Hoyer said Tuesday that Democrats are aiming to bring their policing reform package to the House floor for a vote in about two weeks, during the week of June 22.

       The target date is a week sooner than the US House of Representatives had previously planned to return.

       The effort comes as the United States is reeling from the recent deaths of several black Americans at the hands of the police, including George Floyd, who died in Minneapolis last month after a white police officer knelt on his neck for more than eight minutes.

       The package — put together by the Congressional Black Caucus, House Judiciary Committee Democrats and Sens. Kamala Harris and Cory Booker — would ban chokeholds, create a National Police Misconduct Registry, incentivize state and local governments to conduct racial bias training for officers, and set restrictions on the transfer of military-grade equipment to local law enforcement entities.

       It also would require federal uniformed police officers to wear body cameras. Also included is an anti-lynching measure that has overwhelming support in both chambers but has been held up in the Senate in recent days as Kentucky Republican Rand Paul has sought to make changes to the legislation.

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       Some Senate Republicans have expressed concerns about the policing package, arguing states and localities should set their own policies.

       House Republicans, meanwhile, are planning to introduce their own policing plan, led by Rep. Jim Jordan of Ohio, a source familiar tells CNN. Jordan, the top Republican on the Judiciary Committee, is working with Minority Leader Kevin McCarthy's office, GOP Whip Steve Scalise, and other members in the conference to write the legislation.

       The source said the bill is "in the very early stages" and members are "considering all options."

       Asked if a bipartisan agreement on the matter is possible, Hoyer said during his press briefing Tuesday that Republicans will have "full opportunity to engage" with the Democratic legislation before it comes to the floor, suggesting amendments could be added to the bill.

       Congressional Democrats introduced the measure Monday with no GOP cosponsors. Hoyer said it's "premature" to say the package won't be bipartisan in the end.

       "There's time for bipartisan cooperation on this bill. We welcome it and look forward to their thoughts and suggestions," Hoyer said.

       The House Judiciary Committee will hold a hearing on policing practices Wednesday morning, where members are set to discuss the reform proposal.

       CNN's Lauren Fox contributed to this report.

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