The legislation, spearheaded by members of the Texas Legislative Black Caucus, is named after Floyd, a Black man killed in Minneapolis police custody.
Floyd died after a white police officer knelt on his neck for several minutes until and after he lost consciousness.
Abbott has previously said he is committed to working with Floyds family on legislation, and has even floated the possibility of a George Floyd Act at the Legislature.
The caucus George Floyd Act would limit the use of force by officers, requiring them to attempt to de-escalate the situation and banning lethal force if another lesser level of force could have worked, said state Rep. Jarvis Johnson, D-Houston.
Rodney Floyd, the youngest brother of George Floyd, applauded lawmakers Thursday for the proposal, thanking Thompson during the news conference and saying the legislation has so many great things [that are] way overdue way overdue.Jolie McCullough contributed reporting.