TRENTON, N.J. — Gov. Phil Murphy and Senate President Steve Sweeney are both Democrats, but their disagreements, most recently a race-infused clash over confirming Cabinet officers, hint at trouble between two key figures responsible for enacting New Jersey’s roughly $37 billion budget.

Murphy, a first-time elected official who took over from Republican Chris Christie this year, and Sweeney, an ironworker, union executive and the top senator since 2010, agree on a lot, but they also publicly disagree over the governor’s call to raise taxes on millionaires to fund programs and how to dole out education aid.

The clash between them has largely simmered in the background and both emphasize areas of agreement, but they also show no signs of backing off their views.

Their disagreement spilled into the open this week when Sweeney announced he was holding up the nominations of Murphy’s picks for education commissioner and higher education secretary, who are both black, over school funding. Murphy and Sweeney are white.

Asked at an event in Montclair what he thought of Acting Education Commissioner Lamont Repollet and acting Higher Education Secretary Zakiya Ellis Smith’s nominations being held up, Murphy said they were “extraordinary individuals” who should be confirmed. He talked about how Black History Month had just ended and that he was proud of his Cabinet.

He added: “Folks need to look up Lamont Repollet and Zakiya Ellis Smith, because we have two African-American PhDs on our nominated Cabinet,” Murphy said. “It is the most diverse Cabinet ever nominated in our state.”

He added that the delay in their confirmation votes said “nothing” about his relationship with Sweeney.

“But these two folks need to be confirmed and I’m confident they will be because they deserve it,” he said.

Sweeney said race played no role in his decision.

“Phil Murphy is a good man. He’s better than this. This sounds like Donald Trump,” Sweeney said in an interview. “I know he has to regret making that allusion. I have the greatest respect for the governor and he’s a good man. He’s absolutely better than bringing race up.”

Murphy’s office declined further comment, as did Repollet’s. Smith Ellis’s office did not return an email seeking comment.

Sweeney added that he’s putting the ordeal behind him, but that he’s not budging on school funding.

“This isn’t a Steve Sweeney-Phil Murphy fight. It’s a fight over school funding and we are going to work and we are not going to give up until all children are treated quality,” he said.

At issue is the state’s funding formula for school aid. Murphy says he is abiding by the 2008, state-Supreme Court-approved formula, but Sweeney says it overfunds districts that lost enrollment and underfunds those who’ve gained students.

Murphy said at a recent town hall that he’s willing to revisit how his administration awards aide. His budget calls for nearly $284 million in formula aid.

Sweeney said his and Murphy’s staffs were meeting on school funding and he was putting the issue behind him.

“Where I’m at: We’re moving on. I just think it was a mistake and I’m moving on,” Sweeney said.

It’s unclear what effect the clash over nominations could have but experts say friction could be a factor in whether Murphy can achieve his ambitious, liberal to-do list.

“Sweeney has the ability to railroad Murphy’s agenda, and indeed, his reaction to two of Murphy’s cabinet picks is indicative of his willingness to push back on Murphy’s priorities,” said Brigid Harrison, a political science professor at Montclair State University.

Democrats agree on much in the state: Murphy has signed into law additional funding for Planned Parenthood and the Legislature sent to his desk bills that require employers to offer paid sick leave equal pay for equal work regardless of gender.

But other items in Murphy’s self-styled progressive agenda, like a millionaire’s tax, $15 minimum wage and legalized marijuana have so far not budged.

Murphy and lawmakers have until July 1 to enact a balanced budget.