Rhodesian Prime Minister Ian Smith said yesterday he is visiting the United States to actively lobby for American recognition of his beleaguered white-dominated biracial government which is under escalating fire from African guerrillas.

On the eve of his visit, Smith made it clear during a press conference that he intends to take his case before the American people in an effort to persuade them the Carter administration's policies toward his besieged government are wrong.

Smith said he wanted to "put the record straight" on Rhodesia so that the American people could "make up their own minds whether we are right or wrong."

The 59-year-old white leader declared he was "not all that optimistic" about the prospects of an all-party conference that the British and American governments are trying to arrange as a way to end Rhodesia's six-year-old guerrilla war.

It is expected that Smith will come under intense pressure from American officials to attend an all-party conference that includes Rhodesian guerrilla leaders fighting against his government. This was reportedly considered by U.S. officials in granting his visa. But Smith said he had "heard of no conditions" on him in return for getting a visa.

The British and American governments, with the active involvement of the black-ruled African countries of Zambia, Mozambique and Tanzania, are renewing efforts to find a basis for duscussion for an all-party conference. Smith said he had seen "no new proposals" that would make an all-party conference seem closer to reality.

If Smith's pitch to the American public does produce a significant pro-Salisbury government reaction, it could seriously hinder the administration's efforts to convene the all-party conference aimed at stopping the war and eliminating further Soviet involvement on the guerrillas' side in the Rhodesian conflict.

Josmua Nkomo and Robert Mugabe, the leaders of the Patriotic Front ernment, Joshua have criticized the seven-month-old Smith-led biracial government, which includes three black leaders, as not granting true majority rule to the country's 6.5 million Africans and for granting too much power to its minority of 230,000 whites.

Smith argued that "the surest way to end the war is to give us (the salisbury government) recognition . . it's so logical."

He claimed that many of the estimated 8,000 guerrillas now operating in Rhodesia have not laid down their arms because they have been toldby their leaders that "'The British and American governments are on the side of the terrorists and that because of that there is little hope of us ever getting recognition and . . . of us succeeding.'"

The 59-year-old Rhodesian white leader said he would regard his visit a success if he got American support in "bringing in a constitution which is in keeping with what they have been asking us to do for many years."

Smith's remarks on the lawn of his official residence, called Indepednence, indicate that he would be appealing directly to the American public to support the Salisbury government, citing a sense of fair play and reasons cast in the cold war mold.

"I hope we will be recognized and reinstated as a member of the free world which is our correct position. . . We would like to be back playing our role in the major confrontation which (we) think is (taking place) today and that is the one between the free world and the non-free world.

"But if the American and British governments are now no longer interested in establishing democracy in Rhodesia based on majority rule and if . . . they wish to impose a marxist indoctrinated party-state in Rhodesia, then we are heading for trouble," Smith said.

The issue of whether to issue Smith a visa divided the Carter administration which came under intense pressure from Congressional conservatives to allow the Smith visit.

(In Washington, U.S. District Court Judge John H. Pratt denied a request by TransAfrica, a black U.S. lobbying group trying to influence U.S. policy in Africa, for a temporary restraining order blocking the issuance of Smith's visa).

(Pratt said "foreign relations are the exclusive jurisdiction of the president" and that "it's not for us to second guess" the decision to issue the visa. TransAfrica said it would appeal the decision this morning to the U.S. Court of Appeals and, if rejected there, to the Supreme Court.)

He said he was pleased that the State Department had decided to permit him and his three black colleagues in the biracial government, Rev. Ndabaningi sithole, Bishop Abel Muzorewa and Chief Jeremiah Chirau, to "state our case to the American people.

"We want . . . to give the American people the truth and if they still think we are wrong, if they still want to condemn us, that's fair."

But Smith attributed the State Department's decision to pressure from the American public.

"I don't have to tell you that it is because of strong feelings from the people, senators and congressmen, that the U.S. State Department has been forced to change its mind on allowing us to enter United States. Politically, I'm worried about the attitude of the U.S. government . . . I'm encouraged by the attitude of the people."

The premier indicated his hope that this visit might be turning point in the American attitude toward Rhodesia. "This new change for the better is not just a flash in the pan."