GABORONE, Botswana (AP) _ British Foreign Secretary Sir Geoffrey Howe said today Zambian President Kenneth Kaunda's stinging public rebuke would not prompt him to abandon the search for peaceful solutions to the racial conflict in South Africa.

After arriving in Gaborone from Lusaka, Zambia, Howe said Kaunda was much less curt in private than in his public remarks Thursday night.

Howe, touring southern Africa on behalf of the 12-nation Common Market, said Kaunda expressed willingness to take part in a dialogue on starting negotiations between blacks and whites in South Africa.

''I'm in no way tempted to give up the mission,'' the British foreign secretary said.

Howe planned to see President Quett Masire of Botswana before returning to South Africa today.

Kaunda on Thursday accused the U.S. and British governments of conspiring to support South Africa's government in maintaining apartheid and resisting social change.

He told Howe the Western allies had sent ''a clear signal to the racists to carry on with that system ... that they have nothing to fear by way of sanctions.''

Under apartheid, South Africa's 5 million whites dominate the nation's 24 million voteless blacks, and foes of the racial segregation system have called for international economic pressure on South Africa to force its abolition.

The Zambian leader, whose country is a former British colony and a member of the Commonwealth, said Howe was welcome in Zambia as a human being, but not as a representative of Britain.

Howe, asked whether he had considered walking out on Kaunda, said he didn't think that would have been right because ''it's easier to do than walking back in.''

He compared the situation to blacks and whites being on opposite sides of a mountain, and said someone had to bring them to the top.

''It might be my job to sort of lead them halfway up,'' he said.

Kaunda also criticized President Reagan's speech on South Africa on Tuesday, in which Reagan opposed economic sanctions as a means of fostering change.

''If the West is serious in bringing change in South Africa with less bloodshed, Mr. Reagan should not have broadcast his speech,'' Kaunda said. ''Really, Sir Geoffrey, you people will not be forgiven by history.''

Howe, visibly shocked by Kaunda's remarks, told the president that there was ''no foundation whatsoever for your suggestion'' that he was part of a plan to support Botha's government.

Zambia's capital, Lusaka, is home to the headquarters-in-exile of the African National Congress, the main guerrilla group seeking the overthrow of the South African government. The ANC is outlawed in South Africa.

Zambia, like Botswana, is governed by blacks. The economies of both nations depend on neighboring South Africa.

Howe began his tour in South Africa on Wednesday, when he conferred with President P.W. Botha. The British diplomat said he hoped to encourage the South African government to make rapid and peaceful changes.

Black activists in South Africa, including Anglican Bishop Desmond Tutu and leaders of the country's largest labor federation, refused to see Howe and criticized his mission as a delaying tactic.

Reagan and British Prime Minister Margaret Thatcher have said they are opposed to economic sanctions, maintaining they usually don't work and would cause great suffering among South Africa's blacks.

Howe planned to travel this weekend to Lesotho and Swaziland, two small independent nations surrounded by South Africa, and meet with Botha again Tuesday before returning to report to the Common Market and to Mrs. Thatcher.