The well-worn issue of federal aid to Catholic schools has risen anew on Capitol Hill this year, but this time there's a difference.

In past years when the issue has come up, the Catholic school system has been in precarious health, its enrollment declining, its income insufficient to cover costs.

This year, however, the system is relatively stable, and its leaders are saying that, federal aid or not, it will continue.

There are now 9,822 parochial schools in the United States, according to recently released figures. That is a third fewer than in 1965-66, the peak year for the system, but the mortality rate has also declined sharply. Last year 82 schools closed, the smallest number on record, and church administrators believe most of them were killed by lack of students - populations shifts and declining birth rates - rather than lack of funds.

Nonetheless, Catholics, from the hierarchy to the grass-roots, are continuing their fight for a share of the federal education dollar. Their hopes this year are pinned to the Packwood-moynihan bill, which would provide tax credits to parents for tuition payments.

"Realistically we have always known that the main support for Catholic schools is going to come from Catholic parents," said the Rev. John Meyers, president of the National Catholic Educational Association.

"But it's a question of justice," he continued. "Our argument is that the government ought to aid parents in the education of their children."

In Catholic schools nationally, elementary school tuition averages about $200 a year; for high school the average is around $500 or $600 but it can run up to $1,000 or more for some schools.

Tuition is generally adjusted sharply downward for more than one child from the same family. It is more for non-Catholics or Catholics who do not belong to the school's home parish, and thus do not contribute to the Sunday offerings, which defray some of the school costs.

Meyers estimates that "about 5 percent" of the 3,289,000 pupils in Catholic schools today are non-Catholic. Most are from inner-city areas, where black and other minority parents have truned to them in hopes of obtaining a better quality education for their children than is provided by the public schools.

Msgr. Edward F. Spters, an education consultant at Catholic University, made a study two years ago of Catholic schools in the inner areas of 10 cities. In Chicago, he found, such schools had 39 percent non-Catholics, and 55 percent of the total enrollment was black.

Washington, with 65 percent of its inner-city parochial school pupils black, had an overall 26 percent non-Catholic population.

In two of the most populous boroughs of New York City - Manhattan and the Bronx - enrollemnt of "minorities" - black, Spanish-speaking, Oriental, American Indian and "other pupils - rose from 41 percent in the 1975-76 school year to 60 percent for the curernt term.

"If we can, we want to remain in the cities," said the Rev. Patrick J. Farrell of the United States Cahtolic Conference's eduction department. "If we can, we want to give the poor a choice. That's very important for us."

Farrell, a Chicago priest, illustrates the importance of the parochial school to inner-city blacks with an incident he witnessed at St. Bernard's School in Englewood, a black community in Chicago, after Martin Luther King's assassination.

"The public school across the street had every window broken," he recalled of the turmoil at that time, "but the people from the community stood out in front of St. Bernard's and said, 'That's ours. Don't touch that,' and there wasn't window broken."

Parents of children in parochial schools "feel more an ownership of the school" than is the case with public schools, he said.

Irrespective of the success of current efforts to gain some form of federal aid for the approximately 10 percent of American school children who attend nonpublic schools, Catholic schools will continue, Meyers maintained.

"We've going to grit our teeth and do the best we can," he said.