When the prime minister of Zimbawe-Rhodesia, Bishop Abel Muzzorewa, arrives in Washington to see administration officials this week he will be in a more favorable position internationally than he was nine months ago when he and his predecessor, Ian Smith, visited Washington seeking U.S. support for their "internal settlement."

At home, however, Muzozrewa's new government is fraught with tensions and problems.

Muzorewa left Saisbury today and is scheduled to spend Tuesday and Wednesday in Washington.

During his visit last October, discussions with U.S. officials focussed on whether Muzorewa and Smith would go to a peace conference with their guerrilla foes, Joshua Nkomo and Robert Mugabe. That conference did not materialize for numerous reasons, not least of which was the determination of Muzorewa and Smith to hold national elections for a black-led government before any talks with their opponents.

But this week's talks between Muzorewa and U.S. officials in Washington and later with the British government in London are likely to center on changes Muzorewa can make in order to move his coalition government closer to "g"genuine maority rule" -- especially now that the lifting of sanctions and diplomatic recognition by Britain appear likely.

Britain's new prime minister, Margaret Thatcher, has indicated that her government might lift sanctions -- imposed against the former British colony 13 years ago -- in November.

To Muzorewa another sign of the shifting attitude toward his government is Washington's and London's assignment of official envoys to Salisbury a move they refused to make last year.

The lifting of sanctions is no longer regarded as a consequence of a successful settlement to the war in Zimbawe-Rhodesia as U.S. plicy had defined it until recently.

This represents a shift toward the approach favored by the governments in both Zimbabwe-Rhodesia and South Africa. Officials in Salisbury and Pretoria have argued that rallying around the Muzorewa government by lifting sanctions will prompt defections from the Communist Bloc-supported guerrilla forces and eventually require Nkomo and Mugabe to negotiate their incorporation into a "moderate" government in Salisbury.

This viewpoint minimizes the possible Soviet response and the anger and hostility of black-ruled African states to such a development arguing that those African leaders would have little choice but to accept it.

Such an approach has gained prominence among conservatives in the U.S. Congress and the new Tory government in Britain.

U.S. policymakers on suther Africa, either by defalt or design, appear to be taking a back seat to Britan initiatives in Zimbabwe-Rhodesia U.S. officials are expected this week to avoid making concrete suggestions to Muzorewa on what he should do preferring instead that "specific cnditions [for lifting sanctions] should come from Britain," in the words of one diplomat.

But the principal advice Muzorewa will get from the two Western capital will be based on objections to the Salisbury gvernment heard by British envoy Lord Harlch on a recent trip to black states involved in the Zimbabwe-Rhodesia conflict. Paramount among the objections are the continued presence of Smith, a symbol of white minority rule, as minister-at-large and the lopsided power given whites by the new constitution.

Ae first glance, British and U.S. exhortations to Muzorewa to change the constitution so blacks have more political power would appear fanciful, since Muzorewa is beholden to the white-dominated military estalishment and civil service to keep his guerrilla foes at bay.

But there are signs that some whites in the political and business establishment of Salisbury see the need to change the constitution, even if only to appear to be making concessons so London can more easily justify lifting sanctions to black Africa.

Since the April 24 election, Muzorewa's party has enjoyed the largest voting bloc -- 44 seseats -- in the 100-member National Legislative Assembly. Bur Muzorewa has disappointed many middle class blacks failing to introduce a reformist legislative program, instead presenting one that holds out little promise of change for the black majority.

Many such blacks also are discomforted by Muzorewa's agreement to leave wide powers in wite hands by accepting the present constitution.

Meanwhile, the continuation of the war drains Muzorewa's support among the masses of the country's 6.8 million blacks who bear the brunt of the conflict.

Even among some of those who voted for Muzorewa last April there is much sympathy for the "boys in the bush," as the guerrillas are called. The idea of an all-party conference to negotiate an end to the war is still seen as desireable among many blacks who feel the guerrilla organizations deserve a place in the government because it was they who forced whites to end their exclusive minority rule. CAPTION: Picture, Bishop Abel Muzorewa returns supporters' salutes before leaving Zimbabwe-Rhodesia for the United Stated. AP