In his first public statement in 21 years, Nelson Mandela, the jailed leader of South Africa's black underground, rejected today a conditional offer of freedom made 10 days ago by President Pieter W. Botha.

Mandela said he would make no promises until his people were free of the white rulers' segregationist system of apartheid, and he demanded an unconditional release before he would negotiate with the Botha government which claims to seek reform of the system.

"Only free men can negotiate. Prisoners cannot enter into contracts," Mandela said.

His tough statement was dictated in prison to his wife Winnie and read to a crowd of 8,000 at a political rally in a Soweto amphitheater today by his daughter Zinzi, 22, who risked imprisonment under South Africa's stringent security laws for quoting her father in public.

The rally was called to pay tribute to Nobel laureate Desmond Tutu, returned from abroad. For most of the audience, it was the first statement ever heard from Mandela. It is 30 years since he last addressed a meeting in Soweto. His last public statement was from the dock, when he was sentenced to life imprisonment in 1964.

Mandela was interviewed last month by Britain's Lord Bethell, who reported that Mandela had offered to negotiate with the government if it would recognize his African National Congress. In subsequent statements, Botha specified that Mandela would have to renounce violence first.

Today, the crowd roared Mandela's name and that of the underground ANC's exiled president, Oliver Tambo -- who earlier rejected Botha's offer -- when Tutu asked who were their leaders.

"I am a leader by default," Tutu said, implying that he was merely a custodian for Mandela and Tambo. "You have just heard from those leaders, and I must warn the government that there is no hope for peace in this land until they talk to those leaders," Tutu added.

The rally was unusual, reflecting a relaxation of political restrictions by a government that is trying to reduce tensions and open new lines of communication with the black community. A continued commitment to white-minority political control, however, prevents most black leaders from accepting the newly stated positions as genuine.

It was the first time permission was given for an outdoor rally by the United Democratic Front, an alliance of about 700 antiapartheid organizations that the government charges is a front for Mandela's outlawed African National Congress. Until recently, the front seemed about to be banned as well.

Longtime observers noted that it was the first time they could recall an anti-apartheid rally being held without any visible police presence. Yet there was a reminder of the mounting racial tension in the fact that the rally took place a day after a gun battle between police and a group of ANC insurgents in another black ghetto of Johannesburg. One insurgent was killed.

Mandela, 66, who says his organization turned to violence only because it was suppressed after campaigning fruitlessly for peaceful change for 48 years, said of Botha's offer: "Let him renounce violence. Let him say that he will dismantle apartheid."

Mandela set what appeared to be his own conditions for accepting an offer of freedom when he again called on the government to lift its ban on the congress. He also said the rulers should free all political opponents who had been imprisoned, banished or exiled and guarantee free political activity "so that the people may decide who will govern them."

The rally was an ANC occasion in all but name. Leaders of the Democratic Front openly identified themselves with the outlawed organization, and the big crowd chanted the names of Mandela and Tambo and sang congress freedom songs throughout the day.

Zinzi Mandela, who was born after her father's arrest and did not see him until she was allowed a visit at age 16, was hoisted on the shoulders of the dancing, singing crowd for 10 minutes.

Winnie Mandela, whose restriction order was partially relaxed to enable her to obtain Mandela's reply, listened unnoticed from behind the crowd that she was not allowed to join.

After conveying her father's greetings to Tutu, whom he said he "saluted" for winning the Nobel Prize, Zinzi Mandela read:

"My father speaks not only for himself and for his comrades at Pollsmoor Prison, but he hopes he also speaks for all those in jail for their opposition to apartheid, for all those who are banished, for all those who are in exile, for all those who suffer under apartheid, for all those who are opponents of apartheid and for all those who are oppressed and exploited."