In a budget justification document, the Bureau of Prisons, which operates under the Justice Department, said that it had not concluded how much money would be required to put the First Step Act into effect. But it went on to say that fulfilling the law was a “priority” and that the Bureau of Prisons’ budget for re-entry activities “will be prioritized to fully fund the requirements of the act.”

The document also noted that the prison bureau planned to dedicate $147 million in the 2020 fiscal year to First Step Act-related activities, which include the cost of expanding halfway housing, the cost to relocate people and $85 million for the Second Chance Act grant program, which aids states and nonprofits in reducing recidivism.

Despite the assurances from the president on down that the changes remain a budget priority, questions about funding have advocates on the issue concerned and keeping up public pressure.

“The First Step Act cannot fulfill its promise of turning federal prisons toward rehabilitation and preparing men and women to come home job-ready if it is not fully funded,” said Jessica Jackson Sloan, national director of #Cut50, a prisoner advocacy group that worked closely with the White House to get the legislation passed. Ms. Sloan said the group had been meeting with appropriators and talking to White House officials for months “to ensure that the proper funding is requested and appropriated.”

Others who have worked on the issue said it still remained to be seen whether the White House would push for full funding when it comes time to work out appropriations in a spending bill, and whether there would be an effort to make the Justice Department comply with it.

“I hope that the president’s budget has been amended to specifically fund First Step, but there is so much that needs to be done after that,” said Holly Harris, the executive director of Justice Action Network, which has worked with a bipartisan group on criminal justice overhaul efforts. “We need the president to lean in hard on his allies in Congress.”

Ms. Harris noted that her group continued “to be skeptical” that officials at the Justice Department would prioritize the issue. It was not a priority for Jeff Sessions, the first attorney general in the Trump administration, who fought Jared Kushner, the president’s son-in-law, on making it one. But his successor, William P. Barr, said in his confirmation hearing that he would fully carry out and support the law. Mr. Barr has also met with Mr. Kushner at the White House and understands that it is a priority for top officials, White House officials said.