"At the request of the president and following improvements to the legislation that has been secured by several members, the Senate will take up the revised criminal justice bill this month," the Kentucky Republican said. He said he would turn to it as early as the end of the week. 

An unusual coalition of Republicans and Democrats, conservatives and liberals, civil rights groups and the White House have pushed for action on the Senate bill called the "First Step Act."

Despite the bipartisan push to act on the criminal justice bill, the effort had stalled in the Senate. Pressure mounted as President Donald Trump urged McConnell to call up the bill for a vote. Trump welcomed McConnell's decision Tuesday.

"Looks like it's going to be passing, hopefully – famous last words,'' Trump said at the White House. "It's really something we're all very proud of. Tremendous support from Republicans and tremendous support from Democrats. Lot of years they've been waiting for it."