The initial heavy turnout by black voters in Rhodesia's extended parliamentary election this week gives new momentum to a push in the U.S. Senate to lift economic sanctions against that country, a move that could damage President Carter's prestige at home and shatter his efforts to arrange negotiated settlements to two guerrilla wars in southern Africa.

The first phase of the battle could come as early as next week when Congress reconvenes after Easter recess and looks at the results of the Rhodesia voting, which ends tomorrow. The Salisbury government announced yesterday that 49 percent of the country's voting-age population voted in the first three days of balloting.

Carter administration officials are worried that the relatively positive news accounts of the orderliness and size of the voting in urban areas controlled by the government will help trigger an immediate move in the Senate, which turned back an attempt to lift sanctions last year by only four votes before adopting a compromise measure.

That measure, known as the Case-Javits amendment, for sponsors Clifford Case (R-N.J.) and Jacob Javits (R-N.Y.), requires President Carter to lift the sanctions if he determines that free and fair elections have been held and produce a government that has sincerely attempted to negotiate a settlement, with the guerrilla forces headed by Joshua Nkomo and Robert Mugabe.

The conservative push for lifting sanctions, led by Sen. Jesse A. Helms (R-N.C.), has forced the administration into a defensive posture in what is likely to be a three-phase struggle that could turn on Carter's determination to commit his prestige in a risky undertaking.

The administration's strategy at this point it to emphasize publicly that Carter has not prejudged the election results and to urge Congress to wait for his finding on the fairness of the election. He is likely to wait until the first week in June before issuing a determination.

But some of his aides and liberals in the Senate are concerned that a quick move on sanctions could stampede an early vote there. Among the options reportedly discussed at a meeting of the cabinet-level Policy Review Committee in the White House a week ago Thursday is a proposal to have Carter make a presidential statement on the growing threats to his policy in southern Africa.

Sources in the Senate expect the president to rule that the elections do not meet the requirements under the Case-Javits amendments for lifting sanctions. This would touch off the third and perhaps most bitter phase of the struggle, a showdown in the Senate on a new move by Helms and others to restore U.S. trade and financial dealings with the new Rhodesian government despite continuing U.N. prohibitions.

Officials say that the president's senior foreign policy advisers also reviewed at their meeting last Thursday the long-term diplomatic strategy for Rhodesia and decided essentially to continue the U.S. commitment to getting the Salisbury government and the guerrillas to agree to U.N.-supervised elections no matter how the sanctions battle comes out here.

The administration has already moved to shift the emphasis of its policy to obtain more flexibility to keep up with the rapid changes involving the Rhodesian elections, the predicted downfall May 3 of Britain's Labor government and changes in the balance of forces within the guerrilla camp in recent months.

Secretary of State Cyrus R. Vance signaled the change last month with an unexpected Saturday statement that again emphasized the need for U.N.-supervised elections. But both Vance and British Foreign Secretary David Owen, issuing the same statement, dropped mention of the Anglo-American plan for an all-parties conference to negotiate a settlement.

U.S. officials say that the administration has now dropped the plan's complex power-sharing proposals that had been labeled Options A, B and C and that provided for varying degrees of British control over the transition to a new government to include the guerrillas.

Washington now appears to be moving into a far more passive stance and waiting to see if any new elements emerge that would tempt at least some of the black leaders cooperating with Prime Minister Ian Smith in holding the elections into going for their own deal with the guerrillas to end the war.

After having sought to help bring Nkomo and Smith together last summer in an abortive attempt for a truce, U.S. officials now show great interest in the almost certain emergence of Bishop Abel Muzorewa from the elections as Smith's successor as prime minister and in what is seen here as Mugabe's new strength inside Rhodesia and new moderate image abroad.

Nkomo is seen as having lost ground both among the black population in Rhodesia and with the white leaders who tried to negotiate with him last summer but who sent troops into Lusaka this week to try to kill him at his home. They failed.

U.S. officials concede that the final returns will provide a good measure of the political control the Salisbury government has over the population now, since a maximum effort has been made to lure, and in some cases coerce, blacks into turning out to vote. The guerrillas so far have been unable to carry out their threats to disrupt the balloting in government-held areas.

Now expecting a 60 percent turnout among the country's voting-age population, U.S. officials acknowledge that the first two days' television and newspaper coverage of happy voters flocking to the polls "will tend to legitimize the Salisbury government in the minds of many" and provide new ammunition to the proponents of lifting sanctions. These images also will help the Rhodesians in making the voting the focal point of the battle on sanctions.

Muzorewa is also expected to emerge from the elections with increased support from South Africa, which has noticeably hardened its position on cooperating with Western diplomatic efforts in recent weeks. U.S. officials feel that Pretoria is moving toward relying more on military power to resolve its problems.

A South African decision to pull out of its protracted negotiations with the United States and four other Western nations on ending the guerrilla war in neighboring Namibia (Southwest Africa) would trigger African demands for economic sanctions against Pretoria. The administration's gravest fear at the moment seems to be having to fight two seperate battles over sanctions at the same time if the Rhodesian and Namibia efforts fail.