Rhodesian Prime Minister Ian Smith charged yesterday that the continuing terrorism in 'his southern African country is due to the tacit supprt given by the United States and Britain to the guerrillas fighting his transitional government.

"The terrorism continues only because it is supported by the British and the Americans," Smith asserted on the network television program "Meet The Press" (NBC, WRC).

Smith and one of his black colleagues in the Transitional government, the Rev. Ndabaningi Sithole, appeared on the program as part of their controversial, week-long visit here to win American support for their plan to move Rhodesia to majority black rule.

In all their statements since their arrival Saturday, the two repeatedly have stressed, in diplomatic but unmistakenly clear language, the argument they hope to impress on American public opinion.

Stripped to its essentials, this argument contends that the United States, under President Carter, has broken faith with the Smith government by falling to honor understandings and commitments made by the U.S. government before Carter took office.

Specifically, Smith is asserting that his government's plan for majority rule, known as the "internal settlement," embodies the principles of an Anglo-American plan for a Rhodesia solution worked out two years ago by then-Secretary of State Henry A. Kissinger.

Referring to their meeting in Pretoria two years ago, Smith said yesterday that Kissinger "made clear we would have to accept the principle of one man, one-vote if we wanted to be part of the free world."

Coming to terms with that demand had been "a traumatic experience" for the white minority that has dominated Rhodesia since it break with Britain in 1965, Smith acknowledged."But we did change our minds," he said in reference to his plan for the universal suffrage elections that are supposed to take place at the end of the year. He added pointedly: "Now the Americans and British are holding back."

He was talking about the current U.S.-British call for an all-parties peace conference between his government and Joshua Nkomo and Robert Mugabe, leaders of the Patriotic Front guerrilla forces waging war against Rhodesia from bases in neighboring black African countries.

The Carter administration insists it is not hostile to Smith or Rhodesia's white minority. Instead, administration sources contend, they believe that any solution failing to make provision for a sharing of power by the Patriotic Front will lead Rhodesia into escalating civil war and open the way for Soviet and Cuban involvement in southern Africa.

In their TV appearance yesterday, Smith and Sithole repeated their now familiar arguments that the Patriotic Front leaders have spurned all attempts to give them a role in the "internal settlement" and are insisting instead on a total takeover of power in Rhodesia.

That, Smith argued, is because Nkomo and Mugabe fear rejection by Rhodesia'a blacks if they abandon their guerrilla war and take their chances in the elections being prepared by the transitional government.

"They won't accept the decision of the ballot box because they know they will lose," he said."Therefore they insist that a solution should be imposed from the outside."

Both he and Sithole made clear they are suspicious of an all-parties conference because they believe it would become a device for giving the Patriotic Front the power it seeks. By continuing to insist on such a conference, they added, the U.S. and British governments are playing into the hands of the most radical elements in the dispute by encouraging them to continue their terrorist tactics.