resident Reagan today outlined his proposal to grant a tuition tax credit to parents of children who attend private and parochial schools, calling it "a matter of tax equity" for working families.

Ignoring concerns in Congress about granting further tax reductions at a time when estimates of federal deficits exceed $100 billion, Reagan said: "I believe that working Americans are over-taxed and under-appreciated and I have come to Chicago to offer relief."

The president announced the controversial plan to the 14,000-member National Catholic Educational Association, which is meeting here at the huge McCormick Place convention center on Lake Michigan.

While it will be popular with many Catholics whose children attend parochial schools, the proposal is certain to excite the opposition of public education groups who are already battling a wide array of cuts in federal support that Reagan has proposed for the nation's financially squeezed public schools. The national Parent Teachers Association has promised to oppose it.

Sen. Robert J. Dole (R-Kan.), chairman of the Senate Finance Committee, which will have jurisdiction over the proposal, predicted that it won't reach the Senate floor before Congress adjourns. Assistant Senate Minority Leader Alan Cranston (D-Calif.) agreed.

Although Reagan and presidential aides hinted broadly yesterday that he might be willing to accept a new income tax surcharge as part of a budget compromise with Congress, he sent out mixed signals today about his willingness to bend to Capitol Hill pressures for tax increases.

Reagan dismissed congressional concerns that his tax cuts are responsible for the bloated budget deficits as "the moaning you have been hearing in Washington."

"Suggestions to repeal the third year of our tax cut would stifle our recovery and heighten the tax bill for working families," he said.

Later in other informal remarks the president appeared to be more conciliatory, although he told reporters he had not intended on Wednesday to signal support of the surtax proposal.

But when visiting an eighth-grade civics class at a suburban Chicago parochial school after his speech, he said in response to one pupil's question about high interest rates that he did not believe they would come down until he and Congress compromised on a budget for next year. He said he expected agreement "pretty soon."

The tax credit program Reagan announced today would allow parents of private and parochial school students a credit equal to 50 percent of tuition paid up to a maximum of $100 per child in 1983, $300 in 1984 and $500 thereafter. It would apply only to children in elementary and secondary schools although Reagan said he hoped it could be extended to colleges when economic conditions improve.

Families with adjusted gross incomes up to $50,000 a year would be eligible for the full credit and those earning up to $75,000 for some part of it.

Administration officials estimated that initially the program would mean a loss of only about $100 million a year to the Treasury but that it would rise to more than $1 billion annually by the time the credit was fully phased in.

Those estimates did not anticipate any increases in the numbers of children attending private schools. Last year there were about 5 million children in private schools, about 3.1 million of them in Catholic schools.

The nuns, priests, parents and others attending the Catholic educators' convention here rose to their feet and vigorously applauded the president when he announced the proposal.

But there also were currents of dissent in the hall.

About 40 persons wearing purple ribbons on their chests stood in protest for most of Reagan's speech, occasionally issuing muffled queries of "What about the poor?" "What about the unemployed?"

As he began speaking, one group of about a dozen protesters unfurled a large banner that read: "Arms Race=Theft From the Poor," and they sang, "God hears the cries of the poor. Blessed be the poor," until a priest angrily snatched the banner from them.

Clearly anticipating the strong sentiment in the hall against the nuclear arms buildup, Reagan had added to his prepared speech remarks saying he also shared their desire for peace.

"And whatever we're doing in Washington today in this regard," he said, "is aimed at one purpose and one only--to make war impossible and never again have to lead a generation of young Americans on the battlefield."

Reagan argued that strengthening private schools through tax credits would spur public schools to improve, saying:

"The Pledge of Allegiance, now missing from too many of our classrooms, concludes with the affirmation that we are 'one nation under God, with liberty and justice for all.'

"Private education is no divisive threat to our system of education. It is an important part of it . . . . Excellence demands competition among students and among schools. . . . Let's remember, without a race there can be no champion, no records broken, no excellence--in education or any other walk of life. . . . as competition has lessened, so has quality."

The president told the civics class that he believed the proposal was constitutional and would not violate mandates separating church and state because the tax relief was being granted to parents and not the schools.

The president and administration aides went to great lengths to say that the plan would not give tax breaks to parents of children who attend schools that discriminate on the basis of race or national origin although they were vague on how this would be enforced.

In this city of Irish and Polish Catholic immigrants there has been a long tradition of parochial schools and Reagan noted that in his speech. He also singled out for praise a progressive and highly regarded black Catholic school in a poor neighborhood of Chicago's South Side, Holy Angels.

However, after his speech it was neither to Holy Angels nor to any school in this city's rich ethnic neighborhoods that he went, but to the Catholic school in the well-to-do town of Geneva, Ill., on the remote, heavily Republican western fringes of the Chicago suburbs where he answered questions about inflation, interest rates, taxes and gun control.