Zimbabwean Prime Minister Robert Mugabe said today he was "disappointed" at the $45 million in aid that the United States had offered his newly independent nation and expects American assistance to total "as much as a billion dollars spread over three to four years."

In his public criticism of American policy since taking office two weeks ago, the leader of this key southern African nation also voiced disappointment that the United States did not send "a high-powered delegation" to the country's independence celebrations last month. He unfavorably compared the U.S. team led by former ambassadors Averill Harriman and Andrew Young to that of Britain, which sent Prince Charles and Foreign Secretary Lord Carrington.

The former guerrilla leader received most of his aid from communist countries outside the Soviet Bloc during the seven-year Rhodesian war but has openly turned to the West while keeping the Soviets at arm's length since his election in February.

Speaking in an interview, he was careful to qualify his criticism of the United States and balanced it with remarks that could hardly satisfy the Soviet Union.He appeared to be maneuvering to get substantial assistance from both superpowers as he begins the task of rebuilding his war-torn country. f

Zimbabwe's economy faces a difficult recovery from the aftereffects of the guerrilla war, which cost an estimated $900,000 a day. Furthermore, slack worldwide demand for copper, nickel and chrome forced many layoffs and mine closings in recent years, resulting in high unemployment and a dip in the gross national product. In addition, the war fueled a surge in white emigration, which strained the nation's relatively sophisticated economy.

From all indications, Washington is unlikely to provide anything like the amount of aid Mugabe envisages because of domestic economic considerations and East-West military issues sparked by the Soviet invasion of Afghanistan.

So far, the United States has given $2 million for the rehabilitation of provincial medical services, promised $13 million during the current fiscal year ending Sept. 30 and has proposed another $25 million to $30 million for next year, pending congressional approval.

Jeff Davidow, U.S. charge d'affaires, said the 17-month allocation of as much as $45 million was one of the largest U.S. aid programs for a black African country and shows the serious U.S. interest in Zimbabwe's future.

Mugabe said he could not estimate when the Soviets would be allowed to set up an embassy in Salisbury, since it depended on negotiations.

When it was pointed out that the Americans were the first to open an embassy in Zimbabwe, Mugabe said, "It was only after the elections that they [the Soviets] tried to liaise with us and only during the [independence] celebrations did they really submit their request to us for a mission."

"Naturally, first come, first served . . . They can't complain."

He indicated that the key condition in the negotiations with the Soviets was that they cut their close ties to the Patriotic Front political party of rival guerrilla leader Joshua Nkomo, who has joined in a tenuous government alliance.

Diplomatic relations, Mugabe said, must be "between governments and not between political parties."

The prime minister's remarks on American assistance were occasioned by a comment yesterday by Finance Minister Enos Nkala that so far U.S. aid amounted to "peanuts."

The soft-spoken leader, sitting in the office formerly occupied by his white predecessor, Ian Smith, did not mince words. "We are all-around beggars at the moment," Mugabe said. "We need peanuts, too -- nearly every form of aid that's given us."

Zimbabwe's "expectations were very high" for American aid, he said, because of the billion-dollar development fund that was part of an Anglo-American settlement proposal in 1977-79 that never came to fruition.

"So when we get the impression the United States is no longer prepared or kind of retracting from that commitment, we naturally get disappointed."

He noted, however, "the friendship that has been shown us over the last two or so months" by the United States and hoped that it would continue.

"I want to believe this is an indication of more substantial aid coming," Mugabe said, adding: "I would expect as much as a billion dollars spread over three to four years." He said Zimbabwe had made a general appeal to all nations because of the need to reconstruct the country after the war. "There is no country we have not approached so there won't be any country to turn to if the United States turns us down. It means we just continue asking others."

No direct approach has been made to the Soviet Union aside from the general appeal, but Mugabe said he would expect "substantial" aid when talks are held with a Soviet delegation scheduled to come here.

He added, however: "We want aid without strings attached; aid to enable us to become our own masters, not to turn us into puppets."

On other matters, Mugabe:

Said he wanted to establish a socialist state in Zimbabwe, but one "that accepts a role for private enterprise." Having inherited a capitalist system from the white-minority government, he said there would always be private enterprise in the country as long as it benefited the people and was fair to workers.

Said Zimbabwe would not pattern itself after any nation, but he added that he preferred the current situation in China, which has relations and aid with both the West and communist countries.

Welcomed foreign investment as long as most of the profits were reinvested or local owners had a majority interest.

Said no decision had been made yet on whether to allow the South African diplomatic mission, established during Smith's illegal white-minority government, to remain in the country.