In a gesture that symbolized the purpose of his three-nation tour of Africa, Soviet President Nikolai Podgorny flew today to the demarcation line between black and white Africa - the mighty Victoria Falls on the Zambezi River that divides Zambia and Rhodesia.

From the cliffs that plunge 273 feet to the river gorge, Podgorny and his Zambian hosts stopped at several points during the half-hour walk to look across the river at Rhodesia, one of the last two bastions of white rule in Africa.

At a luncheon speech after his tour, the 74-year-old Soviet president described the falls as "border between the freedom and the slavery which divides today's Africa."

He told his Zambian audience: "We are fully confident that the day is not far off when the freedom and equality will also step across the River Zambezi."

In a reference to recent Western efforts to find peaceful terms for transition to majority rule in Rhodesia, Podgorny added: "Today in the West there are still many of those fond of interfering under the flag of the struggle for human rights into the internal affairs of other states." The Soviets have sharply attacked President Carter in recent days in similar language for his criticisms of human rights in the Soviet Union.

Former Secretary of State Henry A. Kissinger made the same trip here just under a year ago when the first came to southern Africa to discuss settlement of Rhodesia's 11-year-old constitutional crisis.

Podgorny's visit here today also symbolizes the changes since Kissinger's visit: The deadlock in peace negotiations between blacks and whites over peaceful means of transition to black rule, and the rapid escalation in the campaign by Soviet-supplied guerrillas now waging war against Rhodesia.

A year ago there were great hopes for peace as the West became involved in negotiating the troubles of southern Africa. Now, as Zambian President Kenneth Kaunda said over the weekend, intensified war appears to be the main option for establishing Zimbabwe (the African name for Rhodesia).

Observers and diplomats in Zambia believe this first trip to black Africa by a prominent Soviet leader is aimed at pushing that option by getting a full commitment from three key "front-line" states - Zambia, Tanzania and Mozambique - to back the war and not participate in another series of Western-backed peace negotiations.

These sources point out that Podgorny has been flanked throughout his African tour by Gen. Sergei L. Sokolov, first deputy minister of defense and well-known "distributor" of arms to liberation movements. He is scheduled to be present during Podgorny's talks with Rhodesian and Namibian (South-Western African) nationalists Monday.

During the morning visit, the Soviet president walked through the falls' heavy mist - called Musi-o-Tunya or "the smoke that thunders" by Africans - as far as the bridge that joins Zambia and Rhodesia. His host, Grey Zulu, secretary-general of Zambia's only party, explained. "Where you see the buildings over there, that's Rhodesia." Podgorny, looking through binoculars, said only "ahh."