In a short, unemotional ceremony, Abel Muzorewa was inaugurated today as Zimbabwe Rhodesia's first black prime minister. He appealed for the cooperation of all "true Zimbabwe Rhodesias" with the government he will lead.

In accepting the post reserved exclusively for whites for the past nine decades, the American-educated Methodist bishop inherits a guerrilla war prosecuted by two black nationlist leaders. The nationlists contend that the transfer to black rule is not genuine because of the substantial role the white minority will continue to play in national politics.

Since last month's first all-race national elections, which Muzorewa's United African National Council won, the war continues unabated with an average of a death an hour, adding to the estimated 16,000 to 20,000 victims it already has claimed. Most of the dead are black civilians in the countryside who were caught between government security forces and the guerrilla groups of Joshua Nkomo and Robert Mugabe.

One of the first to congratulates Muzorewa was former prime minister Ian Smith, who defiantly led the breakaway British colony in the face of international opposition to its white rule for the past 15 years.

Smith finally bowed to the pressures of economic sanctions and the war to initiate the negotiations with black leaders last year that led to Muzorewa's appointment today.

"Congratulations, I wish you well and hope you will be very successful," the outgoing white premier told Muzorewa in stiff, proper tones while shaking his hand. Smith has made no secret in the last year of his great personal reluctance to step down and to end white rule in Rhodesia.

Today's historic ceremony opened with a dash of colonial flair when elaborately attired black trumpeters of the British South African Police Band sounded a fanfare. Rhodesia's chief justice, Hector McDonald, in a ceremonial floor-length red cape and a white powdered wig, swore in the new black state president, Josiah Gumede, who was elected Monday.

Gumede than asked Muzorewa to become the prime minister and later offered a toast that must have left the new prime minister wondering.

"Every country has its happy accidents," Gumede said. "You as the first prime minister of Zimbabwe Rhodesia are one of those happy accidents."

In addition to the war, Muzorewa faces dissident voices within his own party as well as the suspicions of blacks who are not of his tribal affiliation and of whites who are waiting to see whether he will honor the constitution drawn up last year by Smith and three black leaders.

No doubt Muzorewa had all these divisive elements in mind when he made his call for united support to about 200 invited guests after reciting the three-part oath of office in a clear, firm voice.

"If there are people who are charged with the responsibility of creating order in their own country, of creating peace and of leading to a prosperous country, those people are no other than those who live in this country. Today I'm looking forward to true Rhodesians . . . Zimbabwe Rhodesians to cooperate with the government that will be announced tomorrow," Muzorewa said.

Although top officials of Muzorewa's party say privately they are putting out feelers to the guerrilla chiefs, there is little hope among observers that a realistic accommodation can be made between Muzorewa and his guerrilla opponents.

"What they say to us privately is differrnt from what they [the guerrilla leaders] say in public," said one Muzorewa party official. "The question is when are they going to start saying it in public?"

The Muzorewa camp, however, is encouraged by what appears to be a growing sentiment to lift the 13-year-old international economic sanctions against Rhodesia both in the new Conservative government in Britain and in the U.S. Senate. In addition, the incoming government already has the full support of South Africa.

Unsmiling and appearing a bit for-lorn, Smith was all alone for a moment in a corner of the manicured lawn outside the president's official residence where the outdoor, midday ceremony took place.

However, he later told reporters, "I'm not the sort of person who will sit around and mope because things haven't gone quite the way I wanted them to.One has to be constructive, look to the future and make the most of the world we live in."

Smith expressed belief that "there's a good chance for a new country. Fortunately we had the time to prepare a good consitution which I hope will make Rhodesia unique in Africa."

Smith is expected to be part of Muzorewa's biracial Cabinet, possibly a minister-without-portfolio. The Cabinet is to be announced tomorrow and take power on Friday when the new constitution, which leaves Rhodesia's white minority in control of the military, judiciary, police and civil service for the next five years, comes into effect.

Under the agreement Smith and Muzorewa made last year, the Cabinet must be a coalition, representing all the parties that gained seats in the national legislative assembly. Muzorewa's party won 51 of the 100 seats and 28 were reserved for whites under the consitution. CAPTION: Picture, Rhodesia's white leader Ian Smith congratulates new Prime Minister Abel Muzorewa and Prsident Josiah Gumede. AP