Britain and the African states opposing the controversial Zimbabwe-Rhodesia government narrowed their differences today in a surprisingly upbeat opening debate at the 41-nation Commonwealth conference.

British Prime Minister Margaret Thatcher and Tanzanian President Julius Nyerere, the key participants in the talks, outlined similar positions on significant areas of the Rhodesia issue, which has plagued Western relations with Africa for 14 years.

Although delegates pointed out that serious differences remained, they talked about a positive atmosphere for progress in contrast to fears before the conference that the organization of Britain and its former colonies could be split seriously over the issue.

Thatcher for the first time agreed with African criticism that the constitution under which Bishop Abel Muzorewa was elected prime minister in April "is defective in certain important respects," and she provided specifics.

British sources were quick to say that there was no change in Thatcher's position and that her policy was simply evolving, but delegates saw the move as a significant shift in her backing of Muzorewa.

For his part Nyerere, the leader of the front-line states opposing Muzorewa's unrecognized government, acknowledged that the election brought about "political change." It was the first time that any key leader of the states supporting the guerrillas opposing Muzorewa has made such a public admission.

A Tanzanian source close to Nyerere said "a lot of narrowing of differences" had occurred in the remarks made by the two leaders today. A British source said the talks had been "extremely constructive and an encouraging beginning."

The advances mean that Thatcher and the front-line states have reached some measure of agreement on moving toward a constitution providing black-majority rule.

It appeared that for today at least both sides chose to accent their agreements rather than the disagreements.

There are still major differences, however, including a cease-fire in the six-year-old war being carried out by Patriotie Front Guerrillas, the disposition of the military forces and whether to replace the Muzorewa government.

In addition, today's talk only involve Britain and the African supporters of the guerrillas, Muzorewa and his white backers and the black nationalist forces opposing him would still have to agree.

Although delegates praised the positive atmosphere, many were cautious, remembering how past optimisim had faded away over the seemingly intractable problem of meeting the conflicting demands of 6.8 million blacks and the white community of 250,000 that ruled Rhodesia until Muzorewa took power.

Nigeria, which just this week nationalized a British oil company's holdings in a Rhodesia-related move, provided the major exception to the optimism. It sharply criticized the lack of specific proposals in the British position so far.

British officials have made it clear that the Commonwealth talks, involving 14 African nations, represent the culmination of three months of consultations by the new British government to find an acceptable solution to the Rhodesia problem.

They say no firm proposals will be made at the conference but rather that Thatcher will return to consult with her Cabinet before announcing her plans "within a matter of days."

Maj Gen. H.E.O. Adefope, Nigerian foreign minister and head of its delegation to the conference, said he saw no change in the British position and added: "If we don't have something concrete to take away from this conference we shall regard it as a failure."

In such a case, he added. "We shall have to reconsider the usefulness of such an organization."

Nigeria, the richest black African nation and Britian's largest trading partner on the continent, has threatened economic relation against London if it lifts economic sanctions and recognizes the Muzorewa government. The British Petroleum holdings it nationalized Tuesday are valued at about $150 million.

The Tanzanian president, acknowledging for the first time that "there has been political change in Rhodesia," said: "There are now a majority of black faces in the Salisbury parliament. There is now a black prime minister and a black president." He called the change "more cosmetic that real," however.

"The real issue" was the constitution which, he said, "does not involve a real transfer of power from the minority to the majority because the levers of government power are put beyond the reach of the Cabinet and retained" by the whites. He specifically criticized continued white control over the judiciary, the civil service, police and military.

Thatcher, in similar remarks about the changes brought by the April elections said: "There is now an African president, an African prime minister and an African majority in parliament."

She also called "valid criticism" African complaints that the constitution is "defective." She cited the power of the white minority in parliament to block changes and "the composition and powers of the various service commission."

"It is clearly wrong that the government should not have adequate control over certain senior appointments," she said.

Thatcher did not mention the issue of lifting economic sanctions which has been the center of attention of conservatives in the United States and Britain who support Muzorewa.

The differences remain considerable, however.

Nyerere called for new elections, saying "it is not possible to introduce a new constitution and to co-opt representatives of the external nationalists into the Salisbury government structure."

Thatvher made no mention of elections or any method of changing the government except to say that the guerrillas should be allowed to return home and "play the full part in political life." In the past she has talked about building upon the structure of building upon the structure of the Muzorewa government, something Nyerere specifically ruled out.

The British prime minister called for a cease-fire to go into effect at the time she makes her proposals while Nyerere only said it should be in effect at the time of elections. That Patriotic Front guerillas say they will not lay down their arms until they have gained power.