Rhodesia's biracial government announced in Salisbury yesterday that it has ordered an end to racial discrimination in public facilities, but will keep separate educational and health systems and laws that segregate residential neighborhoods.

Affected by the desegregation order are such public places as hotels, restaurants, cafes, theaters and swimming pools. Restrictions on commercial activities by blacks in industrial areas also were lifted.

Bishop Abel Muzorewa, a black member of the ruling Executive Council, said more racial barriers will be removed "as soon as the people who are working on it" are ready with the next stage." He would not give a timetable.

The end of the racial discrimination was one of the goals of the biracial government formed March 3 by Prime Minister Ian Smith and three black leaders. The four have been criticized for not moving more quickly. Yesterday's action fell short of expectations, held by many, that all forms of segregation would be eliminated.

The Rhodesian government apparently chose to retain all-white schools, hospitals and neighborhoods in order not to upset the 230,000 whites remaining in Rhodesia at a time when their morale is plummeting and there are signs of a backlash against the March 3 agreement. Whites are beginning to feel that in return for agreeing to majority rule, they have received nothing but continued international hostility and an escalation of the guerilla war by the two black nationalist leaders opposed to the settlement, Joshu Nkomo and Robert Mugabe. There are even fears that the so-called internal settlement may be rejected in a whites-only referendum scheduled next month.

The government's concern for white morale and confidence was criticized in a document released yesterday by the Roman Catholic Church's influential and Justice Commission.

"The members of the transitional government, blacks and whites, seemed to be more concerned with white morale and confidence than building a new social order," the church group's document said.

The commission blame the government for the worsening war situation and criticized it for failing to reach all but a few of its "limited aims." The document said Smith was "deeply embarrassed" by the failure of "at least two" members of the Executive Council to persuade guerrillas led by Nkomo and Mugabe to lay down their arms. This was a reference to statements by Muzorewa and the Rev. Ndabaningi Sithole that they would be able ot convince the guerrillas to accept a ceasefire proposal made in.

An official of Nkomo's political party, the Zimbabwe African Peoples Union, belittled the government's action yesterday, calling it "irrelevant." Willie Musarurwa, the publicity secretary of he union, said it was "too little, too late."

Meanwhile the South African press agency, quoting informed sources, said that a recent meeting in London between Nkomo and the third black member of the Executive Council, Chief Jeremiah Chirau, may signal a renewed effort to arrange talks between the government and th e guerrilla factions.

Chirau refused to confirm or deny that the meeting took place.

In London, British officials have said Foreign Secretary David Owen foresees a trip to southern Africa late this month to try to set up an all-party conference.

Rhodesian government officials and Western diplomats in Pretoria said they knew of no concrete plans for a conference, although one informed source said there are expectations of "some realignment" of the forces in Rhodesia which "would make a broader agreement possible." The hope, long nurtured by those involved in the Rhodesian question, is that Nkomo will agree to join the internal settlement, even if his guerrilla partner, Robert Mugabe, chooses to fight on.

So far, Nkomo has rebuffed overtures from the government, which would welcome his participation because it would increase the government's credibility.

The armies of Nkomo and Mugabe have escalated their guerrilla war in the hope of preventing elections in Rhodesia this year. The war was carried into the heart of Salisbury's neighborhoods last weekend when guerrillas robbed a store and threw an explosive device at customers in a beer hall, wounding six persons.