New York City Public Advocate Jumaane Williams praised Mayor Eric Adams’ State of the City speech Wednesday, but said he will work to push the mayor not to cut from key areas of the budget.

“I think we’re going to have to look at some of the details that come out of it, but overall, I felt like the mayor was describing a city that most of us want to live in and describing a government that should be working to help that happen,” Williams told Errol Louis on “Inside City Hall” Thursday.

Adams will join “Inside City Hall” Friday evening to offer his own perspective on his speech and 2023 agenda.

On Thursday, the public advocate said he wants more details on the structure and funding of the mayor’s mental health initiatives, as well as further insight into Adams’ housing plan.

At his speech inside the Queens Theatre in Flushing Thursday, Adams reiterated his call for 500,000 new homes to be built in the city. Williams wants to know how many of those will be affordable and how much the mayor plans to focus on preserving the city’s existing housing stock.

“If we want to make it easier to build, we should be focused on the lower-income bands that actually need the most help,” Williams said. “And also, there is no housing plan that’s real if at least 60% of that is not about preservation, preserving the units we already have.”

Williams warned against “moving into austerity cut times,” but conceded tough budget decisions were ahead. Key departments and roles, like that of inspectors assigned to the Department of Buildings and the Department of Housing Preservation and Development, need to be funded in order for the city to reach its goals, he said.

“We do need additional revenue. It’s going to be hard to push the lofty goals that I’m hearing in the city and the state — and they’re goals that we need — it’s going to be hard to do that if we’re saying we’re cutting everything and if we’re going to say we can’t raise any revenue,” Williams added.

He plugged the Invest In Our New York Act as his preferred solution to revenue shortfalls.

The proposed state legislation — backed by progressive organizations and policymakers — would raise taxes on New York’s millionaires and billionaires, and richest corporations, to fund new spending projects.

“We want to make it so that people aren’t penalized for success, but we do want to make sure that there are folks who need assistance in our city — literally cannot eat, literally cannot get health care,” get the help they need, Williams said. “Then there are folks who actually can do a little bit more, and we have to have a conversation with them about civic responsibility.”

The mayor has previously resisted calls to raise taxes on the richest New Yorkers.

One issue where Williams and Adams do see eye to eye on is the need for the federal government to step in to help the city handle the arrival of thousands of asylum seekers.

Williams, city Comptroller Brad Lander, and 28 City Council members sent a letter to President Joe Biden last week imploring the president to expedite additional funding for municipalities like New York City and work permits for asylum seekers, something Adams has been speaking about for weeks.

“What is happening now is unsustainable for the city. Everyone is clear about that,” Williams said. “That’s why we’re asking and pleading for the federal government to give more resources.”

“The state in particular, the governor has been particularly silent on this issue,” Williams added.

However, Williams disagrees with the mayor on whether asylum seekers fall under the jurisdiction of the city’s “right-to-shelter” laws, which mandate the city provide shelter to anyone in need.

In a radio interview Wednesday, the mayor said “we don’t believe asylum seekers fall into the whole right-to-shelter conversation.”

“We can’t change what our moral and legal responsibility is,” Williams said. “When it comes to something like right to shelter, that is the law and it needs to be that way. We can’t start carving people out.”

The public advocate said he spoke to migrants demonstrating outside the Queens Theatre Thursday, noting they were “very happy to be receiving the care they’re receiving,” but some were having issues getting quality food, and some faced possible eviction.

Williams said he hoped to continue to work with the mayor on issues like gun violence, while urging him to address the underlying causes of crime to avoid getting to the point where policing is necessary as much as possible.

“My job as public advocate isn’t for or against, it’s making sure there’s a check on the work that’s being done,” Williams said.