President Reagan said yesterday that his "constructive engagement" policy has "made solid progress" in bringing about change in South Africa's segregated system, but that he will consider suggestions made to him by Bishop Desmond M. Tutu, a leading antiapartheid leader and severe critic of U.S. policy.

Reagan, who met yesterday with Tutu, later announced that the South African government had released 11 of 16 black political opponents detained without charges in early November and claimed it as a victory for his policies.

The detention of these moderate labor leaders and prominent community activists in early November came amid massive detentions and rising violence in South Africa over racial issues and sparked increased concern in the United States for the situation there.

A series of protests and demands for the release of these leaders began Nov. 21 at the South African embassy here and continued yesterday with more demonstrations and arrests in several U.S. cities. But Reagan said he had "no evidence" that the demonstrations had been instrumental in the South African government's decision.

"This is the result of three weeks of work that we have put in with quiet diplomacy, and today it bore fruit and they are released," Reagan said as he left the White House for Camp David. "I don't think that we're being too bold in taking credit for this."

South African Ambassador Bernardus G. Fourie said in an interview that the 11 were released without charges as part of the normal judicial process in South Africa and was not related to political actions in the United States. The five others arrested at the same time have had charges filed against them and were released on bail, he said.

Tutu, emerging from 1 1/2 hours of meetings with Reagan and other top administration officials before the announced release, said the president expressed interest in some of his ideas for promoting change in South Africa but that neither changed the other's mind on the fundamental issue of how the United States should deal with that country.

The administration's constructive engagement policy relies on friendly persuasion to try to get South Africa to change its apartheid system of racial segregation and rejects the use of punitive actions, such as economic sanctions.

"There on sanctions it is quite clear that we are no nearer each other than before we entered the White House," said the black South African bishop and antiapartheid leader.

Tutu has criticized the policy as "immoral, evil and un-Christian" collaboration with South African apartheid and said it made conditions worse for blacks in Africa.

"We had an opportunity to explain to him Tutu the things that we have been doing . . . I think many of them were a surprise to him," Reagan said at an impromptu press conference. "Some of the things that he suggested are things that we're already doing. But there were others that our State Department is taking heed of and we're going to look at very carefully."

Tutu said he told the president he should call for an end to the current violence in South Africa, release of all detainees, a lift on bannings and forced population removal schemes, amnesty for all political prisoners and a national convention to draw up a blueprint for a new kind of society.

"We hope very much that the administration would begin to send signals to the oppressed that would be signs of hope," Tutu said.

Meanwhile, demonstrations continued at the South African embassy here with the arrests of three more protesters, bringing the total to 31. Those arrested here were U.S. Rep. Cardiss Collins (D-Ill.); Sister Mary O'Keefe, a member of the National Board of Directors of the Association of American Nuns; and Santita Jackson, daughter of the Rev. Jesse Jackson.

More than 300 demonstrators joined the embassy picket line yesterday, including four busloads of representatives of the National Education Association, in town for a board meeting.

Six more persons, including Reps. Charles B. Rangel (D-N.Y.) and Edolphus Towns (D-N.Y.), were arrested in antiapartheid protests in New York, three arrests were made in Houston, and two in Boston. Jesse Jackson participated in a pray-in at the South African consulate in Beverly Hills but was not arrested.

Reagan said his policy of quiet diplomacy has "made solid progress" in obtaining changes in South Africa. It is "counterproductive for one country to splash itself all over the headlines" making demands on another government, because that government "can't appear to be rolling over at the demands of outsiders."

Opposition to U.S. investment in South Africa "is based on ignorance," because American companies provide jobs for blacks there, Reagan said.

A senior administration official, who spoke to reporters under the condition that he not be named, said the administration already has spoken out forcefully against banning orders, police violence and the detention of political opponents in South Africa but that officials will do so more frequently to make its position clear.

"If there was one striking impression that both the president and vice president would take in their meetings from these exchanges it would be the point about perceptions and communications," the official said.

"We have a strong policy . . . . We are determined to make it understood. That applies not only here but more importantly perhaps in South Africa amongst various audiences there."

The situation in South Africa has gained more attention on Capitol Hill. Earlier this week 35 conservative Republican congressman said they would support diplomatic and economic sanctions against that country unless there was an immediate end to violence and noticeable progress made on ending apartheid.

Sen. Richard G. Lugar (R-Ind.), the incoming chairman of the Senate Foreign Relations Committee, and Sen. Nancy L. Kassebaum (R-Kan.), chairman of the African Affairs subcommittee, met Thursday with the South African ambassador and called for the release of the 16 leaders.

Staff aides to the senators said that Fourie called them yesterday to let them know of the release of the 11 and that bail had been set at a low rate on the other five.

One knowledgeable government official said the five apparently are being charged for what amounts to "economic sabotage" and let out on bail equal to about $1,000 each.

White House spokesman Larry Speakes said that two of those released without charges were key trade labor leaders Phiroshaw Camay and Chris Dlamini.

Efforts by the administration to gain their release started "vigorously through private channels" on the day they were detained, he said.

Assistant Secretary of State Chester A. Crocker met two weeks ago in South Africa with four cabinet leaders in four separate meetings and "stressed the urgency of the U.S. government's desire that they be released and . . . expresssed the president's personal interest in it," Speakes said.

The president did not talk personally with South African officials, he said.

Those meeting with Tutu and his wife Leah included Vice President George Bush, Secretary of State George Shultz, Crocker, White House counselor Edwin Meese III, White House chief of staff James A. Baker III and National Security Affairs adviser Robert C. McFarlane.

Tutu, describing his meeting with Reagan in diplomat's language, called the discussions "full, frank and friendly."