Secretary of State Cyrus R. Vance made a strong new plea yesterday for Rhodesia's biracial transitional government and its guerrilla foes to accept United Nations-supervised elections as a means of ending the escalating bloodshed in the southern Africa country.

Vance's appeal, issued with a similar statement in London by British Foreign Secretary David Owen, reiteratd the Anglo-American view that the elections planned for April 20 by white Prime Minister Ian Smith's government cannot provide a solution that will move Rhodesia to black majority rule without "a protracted and damaging war."

Smith's election plan has been rejected by the Patriotic Front guerrilla forces fighting his government from bases in neighboring Zambia and Mozambique. The front's leaders, Joshua Nkomo and Robert Mugabe, contend that the elections are a sham designed to elect puppet officials through which fewer than 200,000 whites can continue to rule over Rhodesia's 6 million blacks.

The Vance and Owen statements were somewhat unexpected because U.S. officials have been saying for several weeks that there appeared to be no chance of successfully getting the contending factions in the Rhodesian dispute to work out their differences in a so-called all-parties conference.

Diplomatic sources said the sudden shift was prompted in part by pleas from Carter administration supporter in Congress for a new, high-level expression of concern. Backers of the administration's southern Africa policy are fearful of growing congressional pressure to accept the results of the April 20 balloting and end the long U.S. refusal to recognize the Rhodesian government.

Legislation passed last year requires President Carter to extend recognition and lift U.S. economic sanctions against Rhodesia if he determines that the Smith government has made a good-faith effort to negotiate with the guerrillas and if the April elections are conducted in a way that allows all parties to participate on a one-man, one-vote basis.

Last week, the Senate Foreign Relations Committee adopted a resolution, offered by Sens. George McGovern (D-S.D.) and S. I. Hayakawa (R-Calif.), calling for the sending of 25 to 50 observers, chosen from outside the U.S. government, to go to Rhodesia and report on the April voting.

If the McGovern-Hayakawa plan is adopted by Congress and the American observers render a favorable report on the election process, congressional pressure on Carter to accept the results is likely to become irreversible. That, in turn, would be a major blow to the administration's carefully cultivated relations with the countries of black Africa, which insist that the Patriotic Front have a role in any Rhodesia solution.

These factors were obviously on Vance's mind when he appeared before reporters yesterday to read one passage from his lengthy statement. In part, it said:

"We believe that both sides should take a first and significant step: to accept the principle of U.N.-supervised elections in Rhodesia, and to agree to negotiate the conditions for holding such elections....

The crucial point is the acceptance of the principle of internationally supervised elections as the only way to avoid protracted and damaging war."

"We would prefer that negotiations begin prior to the April 20 elections," he added. "Failing that, we would hope that the principle of U.N.-supervised ELECTIONS WOULD BE ACCEPTED BY ALL THE PARTIES BEFORE April 20."

The statement went on to promise that Carter will "faithfully make" the congressionally required determination about the fairness of the April elections, "taking into account all the information available to him." It also declared the administration's neutrality on the McGovern-Hayakawa plan, saying:

"The administration will not be sending its own observers to these elections, since to do so could be to imply official recognition of elections we do not believe can provide a solution to the conflict. The question of congressionally sponsored observers is a matter for the Congress to decide."

Vance's statement then added: "Let me state clearly that the United States government would support the lifting of sanctions against Rhodesia when an agreed-upon and irrevocable transition leading to U.N.-wupervised elections has begun."

Although Vance refused to answer questions, a State Department official said later the new appeal was being made because of U.S. and British perceptions that the opposing Rhodesian factions may be starting to realize that the April elections, whatever their outcome, "are not likely to solve the problem and bring an end to the conflict."

The official noted the escalating terrorism that has forced the Smith governmetnt to put 90 percent of Rhodesia under martial law and to stage heavy raids in neighboring countries. The United States, the official added, "is concerned that the very fact of the elections may make for greater intransigence by all concerned" and prevent substituting a "political dynamic" for the violence.

The last Anglo-American attempt at resolving the conflict came alter Smith made a controversial visit to the United State in October. After discussions with Vance, he and his three black partners in the transitional government agreed to take part in an all-parties peace conference "without preconditions."

Subsequent U.S. and British efforts failed, though, to work out ground rules acceptable to the different factions, and the drive for a conference was put on the back burner until its revival by Vance and Owen yesterday.

The State Department official said no decision has been made yet about sending emissaries to sound out the various parties on the new appeal. Any follow-up action, the official said, will be determined by how the Smith government and the Patriotic Front react to yesterday's statements.