British Prime Minister Margaret Thatcher held her first talks today with Prime Minister Abel Muzorewa, but there was no indication that he was convinced of the need to Broaden black power in his Zimbabwe-Rhodesian government.

Both sides declined to disclose details of the talks. A joint statement said they had discussed "ways of making progress toward . . . bringing Rhodesia to legal independence with wide international acceptance," adding that they planned future talks.

It was known, however, that Foreign Secretary Lord Carrington, who also met with Muzorewa, passed on to film African demands that he reduce the powers reserved in the constitution for the country's 250,000 white minority. Bishop Muzorewa has opposed such moves on the ground that it would lead to an exodus of whites who form the backbone of the military and civil service.

Britain is waiting until after consultations at nex month's Commonwealth conference in Lusaka, Zambia, to issue its own proposals. These are expected to call for Muzorewa to seek revisions in constitutional provisions maintaining white control over the military, police, civil service, judiciary and the process for amending the charter.

Britain is thus in the unusual position of attempting to persuade a reluctant black leader to take more power for blacks.

Today's talks apparently dealt with suggestions that white former prime minister Ian Smith should resign from Muzorewa's government as part of a settlement and that Muzorewa hold talks with representatives of the Patriotic Front, which has been conducting a guerrilla war for six years. British officials, however, refused to comment.

The meeting with Thatcher, which British sources described as "extremely friendlt," lasted an hour. It was understood that she had been available for longer talks if necessary.

Muzorewa, looking grim, refused to speak to reporters after the talks, although yesterday his aides had indicated that he would hold a press conference. It is expected that he will issue a statement before leaving for South Africa Saturday afternoon after a week of talks in Britain and the United States.

Muzorewa also had a working lunch and met for 90 minutes with Carrington, Lord Harlech - who visited African nations recently to test opinion about the Muzorewa government and other senior British officials.

British sources emphasized that the talks dealt with the return of Rhodesia to legality, meaning recognition and an end to its breakaway status since 1965. Under pressure from her own Conservative Party backbenchers. Thatcher is expected to let economic sanctions against Rhodesia lapse in November despite African protests. She maintains, however, that a return to legality can only come after widespread international support for Muzorewa's now unrecognized goverment.

Muzorewa talked to President Carter Wednesday at Camp David - a discussion Thatcher reportedly persuaded the president to hold. It was the first time an American president had met with a Rhodesian leader.

Carter reportedly pressed for a significant broadening of black powers to gain international acceptance as the British are informally doing. The president, who has a surfeit of other political problems and is under domestic conservative pressure to lift sanctions, urged Muzorewa to work closely with Britain to reach a settlement.

This, in effect, puts Thatcher in the position of trying to modify and sell to Rhodesia's black neighbors the controversial settlement plan Smith negotiated with Muzorewa and other moderate black leaders last year.

The major difference is that the Patriotic Front of Joshua Nkomo and Robert Mugabe is now on the outside with apparently no alternative but to carry on the war since they refuse to deal with Muzorewa as prime minister. Thatcher has clearly made Muzorewa the chosen instrument of her settlement policy.

Strangely, Smith could still play a role in gaining African acceptance for Muzorewa by persuading whites to modify their entrenched privileges. This could boost Muzorewa's stature, leading to defections from guerrilla ranks and possibly some African recognition.

For the West the overriding concern is to gain a negotiated settlement to end the guerrillia war. That can only be done with the cooperation of the neighboring African nations that support and harbor the guerrillas.

Escalation of the war would gravely increase the risk of East-West confrontation in Africa over Zimbabwe-Rhodesia, with the Soviet Bloc backing the guerrillas, and the West on the side - in African eyes - of the colonists.