Pope Benedict XVI will arrive in the city next week on the heels of some embarrassing news: a new report warning that inner-city Catholic schools in America could disappear within the decade, and a strike by at least one union of Catholic school teachers.

A union that represents teachers at 10 high schools in the city and Westchester, the Lay Faculty Association, decided to strike late last night after failing to reach a consensus on their demands during a meeting with the Archdiocese of New York.

Many Catholic school teachers in New York have been without a contract since September following disputes over salary levels and an effort by the Archdiocese to increase medical insurance premiums.

Another, larger union, the Federation of Catholic Teachers, halted a two-day strike Monday and is meeting with the Archdiocese Friday morning in an attempt to end ongoing conflicts, but if the health coverage issue is not resolved, the strike could resume, the group’s union organizer, Eileen Sweeney, said yesterday evening.

The federation represents teachers at 209 elementary schools and 17 high schools in the Archdiocese of New York and five schools in the Diocese of Brooklyn.

The labor news comes as a report is being released Friday by a national think tank based in Washington, D.C., the Thomas B. Fordham Institute, concluding that 1,300 inner-city Catholic schools have closed since 1990, displacing about 300,000 students, and that, if demographic patterns keep up, almost all such Catholic schools could be gone by 2018.

Fordham’s vice president, Michael Petrilli, said the downsizing is most dramatic in New York City, where the pope is scheduled to arrive April 18 for his first visit to America. “In terms of the scale, it doesn’t get much bleaker than New York City,” he said.

“It’s a crisis for Catholic education and it’s a crisis for American education. This is a crisis for the cause of educating poor and minority kids,” Mr. Petrilli said.

The latest local Catholic school closures were announced in March, when the Archdiocese said it planned to shut down six elementary schools this June — including one in the Bronx and several others outside the city — and merge four other elementary schools, including two in the Bronx, into two schools for the next year.

The Archdiocese said the closures were a result of “escalating operating costs and declining enrollment all set within the larger context of increased economic pressures on Catholic school families throughout the region.”

The Fordham report also cites demographic change, describing how both demand and labor supply are falling as Catholics move to the suburbs, and the people who historically served as virtually free labor, priests and nuns, leave the teaching workforce.

The city’s recent labor disputes seem to encapsulate those dynamics: The church is saying finances are struggling as tuition lags, while teachers — now largely lay people — are demanding higher pay.

“It’s a philosophy that’s 2,000 years old. They never had to pay people for work,” the business manager for the Lay Faculty Association, Henry Kielkucki, said. “I’ve been told that this is not a job, it’s a mission, and your reward comes in the next life. But I still have to go to the store and buy bread.”

Saying a solution to the Catholic school crisis is sorely needed in order to maintain a positive educational option for inner-city students, the Fordham report presents a solution: Dioceses should follow the model of Wichita, Kan., where tuition at Catholic schools is now free, subsidized by increased tithes paid by church parishioners.

The change has led to a Catholic school revival, the report says.

Said Mr. Petrilli: “The question is, if Wichita can do it, why can’t New York?”

A spokesman for the Archdiocese of New York, Joseph Zwilling, declined to comment late last night, saying he had not read the report.