President Trump began the month hosting a White House celebration with people freed from prison by the First Step Act. He told the April Fools' Day gathering the White House would work on a Second Step Act "right away."

Despite the day, Trump was not joking. But he was also not correct.

Sources tell the Washington Examiner that the White House is in fact not preparing a Second Step Act package to follow the landmark criminal justice reform law, which is Trump's only major bipartisan legislative achievement.

“There’s definitely not a Second Step Act,” said a source who works on White House reform efforts and helped with Trump’s April 1 speech, a draft of which did not mention new legislation.

The White House is focused instead on implementing the First Step Act in a way that denies ammunition to opponents such as Sen. Tom Cotton, R-Ark.

[Related: Prisoners due for release under First Step Act stuck in limbo]

“One of the most important things we do in the second step is to get the first step implemented,” said Mark Holden, general counsel of Koch Industries and a prominent reform advocate.

It is unclear if Trump misspoke when he said: "Today, I am announcing that the Second Step Act will be focused on successful reentry and reduced unemployment for Americans with past criminal records. And that’s what we are starting right away."

A White House official said that Trump "wants to bring more fairness" to the legal system and "you can expect more legislation to address the second steps in the future," but that the First Step Act "will take a year to fully implement," diverting focus from additional legislation.

Between late December and early April, the First Step Act allowed 643 people to leave prison early under retroactive sentence reductions for crack cocaine and because of new compassionate release policies. Future anti-recidivism programming will allow early transfer to halfway homes.

[Also read: Trump says he is undoing Bill Clinton law that was 'devastating' for blacks]

A drafting error in the First Step Act stalled additional “good time” credit for 150,000 federal inmates, creating a likely wave of about 4,000 releases around July. White House officials considered options to move forward the date but ultimately did not.

“There’s a lot of concern that they have to get this right. Folks like Tom Cotton are just waiting for someone to do something stupid,” said the source who has worked on White House efforts. “People are going to want to wait and see how this [First Step Act] works out.”

The White House has pushed businesses to hire former prisoners. In February, Trump's son-in-law and chief adviser on criminal justice reform, Jared Kushner, called Walmart CEO Doug McMillon and asked him to help recently released Catherine Toney and others find work.

Walmart, which already hired ex-prisoners, is working to do more, including helping former inmates overcome poor computer literacy, the company said after Kushner’s call.

Holden said Koch Industries, run by a family of pro-free-market billionaires, has long hired people with criminal histories and is working with the Society for Human Resource Management to encourage other businesses to do so.

“I think the administration is going to do a lot around that with the bully pulpit,” Holden said. He said the legislation has helped “change the mood” toward hiring former inmates.

Holden added that Trump’s support for the First Step Act, which passed the House 358-36 and the Senate 87-12, also triggered reform momentum in states such as Florida and conservative Missouri. State and local governments hold about 2 million inmates.

At the federal level, Holden hopes for White House efforts on clemency reform, such as a commission created without Congress. He also hopes for more legislation eventually.

In a statement, White House spokesman Hogan Gidley emphasized Trump's role in the First Step Act, and the importance of enacting it.

“President Trump was able to secure passage of the First Step Act after politicians failed to do so for 20 years — and we are now focused on full proper implementation to ensure those who re-enter society obtain good jobs and never return to prison," Gidley said.

Holden gave a similarly upbeat assessment. “If you told me two years ago that we’d be talking about ‘Well, the Second Step Act hasn’t happened yet,’ that means the First Step Act did happen, and that’s a big deal," he said.