CHICAGO — Gov. Rick Snyder of Michigan appointed a new emergency manager on Tuesday to oversee the Detroit Public Schools, the fourth such state-assigned manager to lead the struggling system since it was deemed in serious financial trouble in 2009.

While the city of Detroit itself emerged late last year from emergency management and the largest municipal bankruptcy in the nation’s history, some city and state officials worry that the woes of its public schools threaten to slow efforts to remake Detroit and lure desperately needed new residents.

And so, while Mr. Snyder announced that the public schools would remain under the oversight of an appointed manager despite opposition from some school leaders who say control should be returned to the local authorities, he also made it clear that his administration and other officials would soon weigh broader changes for a school system that has wrestled with declining enrollment, disappointing test scores and financial deficits.

“Detroit is making a tremendous comeback in terms of an economic revival,” Mr. Snyder said. “But to have us have long-term success, to have a truly great city, we need an educational system, a system where our students living in the city can get a wonderful education, where they can grow up in a neighborhood where they can say, ‘I want my kids to grow up in that neighborhood.’ ”

The Detroit Public Schools’ problems are longstanding and complex — more, apparently, than even three emergency managers over nearly six years of state control could fix. Over the past 20 years, the schools have lost students and funds to an array of forces: families moving away, policies that allowed students who lived in Detroit to go to suburban schools, the arrival of charter schools in Detroit and its suburbs, and the transfer of 15 schools deemed to be failing into oversight by a state-led authority.

While a spokesman for the schools, Steve Wasko, said the enrollment drop had slowed significantly in the past two years, the numbers are stark. About 47,000 students in kindergarten through high school attend Detroit’s 97 schools now, compared with 96,000 in existing schools in 2009.

About 35,000 Detroit students attend charter schools in the city, officials said, and thousands more attend charters in the suburbs.

On the financial side, too, the problems have barely improved. In 2009, the school system was found to have a $327 million deficit; this year, after managers vowed to carry out an array of cuts and changes, the deficit was estimated at $169.5 million.

And while some in the city’s schools say test scores and academic achievement have improved in the past few years, some national assessments of fourth and eighth graders show that fewer than half of the students are considered proficient in math and reading.

“The data are devastating,” said Amber Arellano, executive director of the Education Trust-Midwest, an education advocacy and research organization based in Royal Oak, Mich. “There’s no other way to cut it. It’s abysmal.”

Mr. Snyder had to decide immediately what to do about the future of the Detroit schools leadership. Under state law, a governing body can remove an appointed emergency manager after 18 months, and Mr. Martin’s time was to run out this week. Critics of state oversight had urged Mr. Snyder to return the schools to local control, asserting that the outside oversight was undemocratic and impractical; a fourth emergency manager would be no more capable of fixing things than the three before him had, they said.

State officials say the intent of Michigan’s emergency manager law has always been to swiftly steer cities and schools systems out of financial distress and back on their own, but Mr. Snyder said the problems in the school system were so great that an emergency manager must remain.

Since 2013, Mr. Earley was an emergency manager for the city of Flint, and he worked as Saginaw’s city manager before that.

“We don’t walk away from problems that took decades to get there,” Mr. Snyder said. He added at another point: “These issues didn’t come about in the course of several 18-month periods. These conditions came about because of decades of challenges.”

Asked whether bankruptcy might be an option for the school system, as it was for the city, Mr. Snyder firmly said no. He noted that a group of community and education officials had begun meeting to sort through larger educational solutions for Detroit, and suggested that wider change might soon be ahead.

“Let’s work through something that can be a better answer in terms of a longer-term answer,” Mr. Snyder said.