A sought-after Lower Manhattan high school has changed its admissions rules just weeks before applications are due, in an effort that school officials say is aimed at increasing diversity.

Until now, Millennium High School has given top preference to students living below Houston Street, then prioritized students living elsewhere in Manhattan. According to the city, just four students from outside the borough were offered a seat at the school last year.

That didn’t sit right with school officials, who asked the city this spring to eliminate the preference for Manhattan students from above Houston Street. The education department approved that request — months later, on the Tuesday before Thanksgiving.

“It came at the 11th hour,” Kathy Lee, Millennium’s parent coordinator, said about the approval. “It’s not the most timely change.”

The change shouldn’t affect how students rank schools on their high school application, due Dec. 3. The city’s algorithm is designed to work as long as students rank schools they are eligible to attend in the order they’d like to attend them.

Still, it is likely to reduce some Manhattan students’ chance of admission — and is sure to create anxiety among eighth-graders as they learn that admissions rules are changing as the deadline nears. Lee said she has been fielding calls and emails from anxious families ever since the school updated its website last week, she said.

The shift also highlights a tension in the city’s efforts to increase school diversity. When community school districts put forth plans to integrate schools, as has happened recently in Manhattan’s District 3 and Brooklyn’s District 15, those changes affect only elementary or middle schools and are made after public conversation. Admissions rules for high schools, on the other hand, change at individual schools’ request, and they follow an opaque process and timeline. (One big exception: Mayor Bill de Blasio’s proposed changes for the city’s specialized high schools, which use a separate admissions system.)

“Schools make decisions about admissions priorities in collaboration with their superintendent and the Office of Student Enrollment,” a city education department spokesperson, Will Mantell, wrote in an email.

“Millennium leadership worked with the Office of Student Enrollment to look at data, and change its admissions priority in a way that worked best for the school community and the goals it is trying to accomplish.”

Millennium is keeping the Lower Manhattan preference, which resulted in students living or attending middle school below Houston Street receiving 70 percent of offers last year. Last school year, city data show that 45 percent of Millennium students were Asian, 31 percent were white, 14 percent were Hispanic, and 6 percent were black.

How the change could increase diversity is unclear. The area south of Houston includes Chinatown, and while Manhattan north of Houston Street has many affluent and white families, it also includes the borough’s largest concentrations of black and Hispanic students. Other boroughs have lower proportions of white and affluent students, but the school could stil easily fill its seats with those students.

A note posted to the school’s website suggests that further changes could come to the school. “This revision, made with the support of Superintendent Richard Cintron and Executive Superintendent Recy Benjamin Dunn, is an important step in promoting equity of access to Millennium,” the note reads.