President Reagan acknowledged today that some parts of the country were experiencing a "near depression" but said that people were much better off than during the Great Depression "when unemployment was total destitution."

In a series of freewheeling appearances, he also expressed doubt about whether Martin Luther King's birthday should be made a holiday, admitted to a cheering audience of black high school students that his attempt to allow tax deductions for segregated private schools was a "beaut" of a mistake, and preached the gospel of volunteerism in this economically hard-hit region of the country.

Defending the federal social insurance and income support programs of which he has often been critical, Reagan said that he understands the "pain of unemployment" but contended that the unemployed today don't suffer the "total destitution" of the Depression because of unemployment compensation and the incomes of working spouses.

The peak unemployment figure during the Depression was 24.9 percent in 1933. It was 9.4 percent nationwide last month but some areas are suffering unemployment of 20 percent or more.

"We have a built-in system, first of all with unemployment insurance and our new welfare programs and so forth, but also the dual employment in families that today, according to Bureau of Labor statistics, it is estimated that only about 30 percent of the families where there is unemployment are without some member of the family unemployed . . . 70 percent of the families have a member of the family employed," the president said.

Answering a question at a meeting of regional editors about the proposed King holiday, the president said he could "understand why the black community would like to do that" but hadn't taken a stand on the proposal because he was concerned that other groups would want similar holidays for their "revered figures."

"We could have an awful lot of holidays if we start down that road," Reagan said.

The president's offhand comment about the King holiday partially undermined another in a series of personal efforts by Reagan to demonstrate that his administration is sympathetic to minorities. White House communications director David Gergen described them as a message to the country "that he is president of all the people."

Today, a major event on the president's schedule was a visit to Providence-St. Mel, a largely black parochial high school on the west side of Chicago that has achieved such a remarkable educational record that the president referred to it as a "shining light."

Sitting alone on the high school stage on a stool, Reagan answered questions about his domestic and foreign policies for half an hour and was resoundingly cheered by the students.

When one asked if he could cite any example of a policy that had turned out contrary to his intentions, Reagan said, "Oh yes, I've got a beaut." He then cited the administration's abortive effort to grant tax exemptions to segregated academies, reversing a policy that was instituted in the Nixon administration.

As Reagan recounted the incident, his plan was merely to prevent "harassment" of schools by the Internal Revenue Service and not to allow tax exemptions for segregated schools.

"I didn't know there were any [segregated schools]," Reagan said. "Maybe I should have, but I didn't and it was a total turnaround of what I intended. Yes, that one went wrong."

Reagan was applauded by the students for this remark and also for his opposition to gun control, which he said existed in Washington and hadn't prevented "that guy who used me for target practice" from wounding him in an assassination attempt last year. He did not mention John W. Hinckley Jr., who is on trial for that shooting, by name.

The president's central message in appearances before editors, black parochial students, Republican contributors and the Chicago metropolitan area YMCA was the familiar one that volunteer efforts can take up much of the slack for government in helping the nation out of its economic troubles.

"We think it will be good for the soul of this country to encourage people to help one another, to get involved, to take personal responsibility for the well-being of their community and neighbors instead of always leaving this to the bureaucracy," Reagan said.

To an unusual degree, the president today used religious metaphors to make his point.

"Christ told his disciples that as you do unto the least of my brethren, so you do unto me," Reagan said. "The message was clear: You serve God by serving those in need. As late as 1935, in the middle of the Great Depression, a substantial portion of all charity was sponsored by religious institutions.

"You might think this is just my interpretation, but in the parable of the Good Samaritan, the samaritan didn't run into town to look for a government caseworker to help the injured pilgrim. He acted directly to do what he could."

In his meeting with more than 40 regional editors the president was challenged on the effectiveness of volunteer programs as a substitute for government help.