Boosted by news that Zambia had decided to reopen part of its border with Rhodesia, Prime Minister Ian Smith and one of three of the black leaders in the biracial government, Rev. Ndabaningi Sithole, left yesterday for the United States.

Smith and Sithole are coming here to lobby for American recognition of their transistional government.

The two men were smiling and joking as they boarded an Air Rhodesia flight at Salisbury airport accompanied by a team of 12 advisers and security men.

In Johannesburg, South Africa, where they changed to a South African Airways flight to New York City, Smith was asked by reporters about Britain's decision to refuse him permission to travel through London.

"I suppose it's the sort of thing one should expect from little people, venting their feelings on personalities as opposed to concentrating on main issues, such as brining peace to Rhodesia and ending the killing of innocent," Smith said.

Smith and Sithole were invited to the United States by 27 senators and yesterday a group of 17 British parliamentarians announced that they have also invited the white leader of Rhodesia's government to visit London for talks.

The group has asked British Foreign Secretary David Own if he would be prepared to give immunity to Smith who faces charges for declaring Rhodesia's independence from Britain unilaterally in 1965. There was no immediate reaction from the government, a spokesman for the parliamentarians said.