Kentucky Republican Sen. Rand Paul on Monday singled out Sen. Mitch McConnell as the one person who can make a vote on the criminal justice reform bill happen and called for public pressure on the majority leader.

Paul, speaking at the Louisville Urban League, said McConnell, the state's senior senator, is the one person who "has the power" to allow a vote on a criminal justice reform bill and said Louisville residents should call his office and say, "Please let us have this vote."

"I will tell you that we need the help of one person. The one person who had the power to allow this vote — and I'm not saying he's stopping it — but there is one person. He's from Louisville, he's fairly well known and he has the power to allow or disallow this vote," Paul said, referring to McConnell.

"There's no reason we shouldn't vote. So I would say if you're in Louisville, call and say, 'Senator McConnell, all we want is a vote'. It will pass overwhelmingly."

Paul has been a zealous advocate for Congress acting on criminal justice reform, often teaming up with unlikely Senate colleagues to bring changes to the system. Last year, Paul worked with Democratic Sen. Kamala Harris of California to introduce a bill that would reform the country's bail system.

In coordination with White House officials, lawmakers have been working on criminal justice reform for the first two years of the Trump administration. "The First Step Act" has the best chance of passing; it currently has 31 co-sponsors in the Senate, both Democrats and Republicans. The House version of the bill passed with overwhelming support in May.

The legislation would implement the most sweeping set of reforms to the system since the 1990s by shortening some long prison sentences and improving conditions for people in prison, among other things.

President Donald Trump tweeted over the weekend that he hopes McConnell will call for a vote on the measure.

Hopefully Mitch McConnell will ask for a VOTE on Criminal Justice Reform. It is extremely popular and has strong bipartisan support. It will also help a lot of people, save taxpayer dollars, and keep our communities safe. Go for it Mitch! — Donald J. Trump (@realDonaldTrump) December 7, 2018

Sen. Chuck Grassley, R-Iowa, chairman of the Senate Judiciary Committee and a sponsor of the bill, tweeted last week that more than half of Senate Republicans support it.

"Ldr McConnell said he would need to have 60+ votes to bring criminal justice reform up & wanted to show large amount of Republican support. We have delivered. More than 1/2 of the Republican caucus supports the First Step Act LET’S VOTE!" Grassley said.

Before the midterm elections, McConnell told reporters he would hold a vote on a criminal justice reform bill if it had enough votes — 60 — to overcome a filibuster.

McConnell spokesman Don Stewart had no comment to NBC News on Monday on Paul's remarks, and gave no indication whether McConnell would schedule a vote in the next two weeks.

Congress has two weeks left in its lame-duck session until lawmakers return to their districts. And before the new Congress is sworn in January, lawmakers are trying to tackle a number of outstanding items, including a must-pass spending package to avoid a government shutdown.

Some conservatives, including Sen. Tom Cotton, R-Ark., oppose the criminal justice bill. Cotton said on Twitter that some of the provisions of the bill are too lenient, suggesting it would allow "repeat offenders with lengthy, violent histories" off the hook.

Dartunorro Clark reported from New York and Rebecca Shabad from Washington, D.C.