Rhodesian Prime Minister Ian Smith yesterday opened his campaign to win U.S. support by calling on the United States, "as leader of the free world," to back his transitional government against "Marxist terrorists."

Smith began his controversial, week-long visit by meeting with reporters and representatives of U.S. conservative political groups at a secluded country estate in this town 75 miles southwest of Washington.

The leader of the white minority government, which the United States has characterized as "illegal" ever since its break from Britain in 1963, said he has complied with the Anglo-American peace plan proposed two years ago by preparing Rhodesia for a shift to black majority rule.

The main priciples of that plan, which were worked out by former secretary of state Henry A.Kissinger, were agreed to by the Smith government in March. But, Smith contended the United States and Britain now have shifted their positions on how to achieve a Rhodesian solution.

"We have complied with our part of the bargain," Smith said. "Now we think it is fair and logical for the American and British governments to keep their part of the bargain."

His words telegraphed the message that Smith intends to hammer away at during a week of appearances that will include a private meeting with Secretary of State Cyrus R. Vance.

The United States and Britain have been insisting that a lasting Rhodesian settlement can only be achieved through an all-parties peace conference that would bring Smith's transitional government into negotiation with the black Patriotic Front force waging guerrilla warfare against Rhodesia from bases in neighboring countries.

So far, Smith and the leaders of the Patriotic Front, Joshua Nkomo and Robert Mugabe, have refused to deal with each other. In the meantime, Smith has ceen moving to implement his "internal settlement" plan that is supposed to produce one-man, one-vote elections for a new government in Rhodesia by the end of this year.

Charging that "our case has been distorted while our opponents have had free access to the American people," Smith said his plan will give Rhodesia a government chosen in free elections on the basis of universal suffrage without regard to color.

"We will create a free, democratic institution where everybody will have their say in the decision," he asserted. "We would have though that would be very much in accord with the desires of the United States. What more do you want?"

Both he and his travelling companion, the Rev. Ndabaningi Sithole, one of the three black members of Rhodesia's interim executive council, charged that the Patriotic Front leaders are terrorists who want to take control of Rhodesia by force and turn it into a state under Marxist influence.

Sithole, formerly an opponent of Smith, said: "What the majority of black people fought for has been won by the internal settlement. The warhas changed from a war between a black majority and a black minority to a war between a black majority and a blackminority which wants to take over power without submitting to the free choices of a general election."

Smith and Sithole, who are scheduled to be joined by the other two executive council members later, were invited to the United States by 27 senators led by S.I. Hayakawa (R-Calif.) The invitation touched off a furious controversy about whether they should be given visas - a step agreed to by the Carter administration on Wednesday only after a long internal debate.

Following their arrival at Dulles airport yesterday morning, they were driven immediately to the meeting here sponsored by more than 20 political and other organizations with a conservative orientation.

Meanwhile, the U.N. Security Council, meeting in private, failed to agree on a proposal calling for censure of the UnitedStates because it issued the visas despite U.N. sanctions against the Smith government.