WASHINGTON — Under pressure from President Donald Trump and many of his Republican colleagues, Senate Majority Leader Mitch McConnell said Tuesday that he will bring legislation to the floor to overhaul the nation’s sentencing laws.

McConnell’s decision comes after more than three years of overtures from a large, bipartisan group of senators who support the criminal justice bill, including Senate Judiciary Committee Chairman Chuck Grassley and House Speaker Paul Ryan. Trump announced his support for the legislation last month, but McConnell treaded cautiously, as a handful of members in his caucus voiced concerns that it would be too soft on violent criminals.

Texas Sen. John Cornyn, the No. 2 Republican, said Trump’s push for the legislation had been “critical to the outcome.”

“Senator McConnell was always concerned about the small window of time that we have to do all these things we need to do, but the president was insistent that this be included,” he said.

If the legislation passes, it could be a rare bipartisan policy achievement for this Congress and the largest sentencing overhaul in decades. AshLee Strong, a spokeswoman for Ryan, said “the House stands ready to act on the revised Senate criminal justice reform bill.” Ryan has long supported sentencing reform and is retiring at the end of the session.