Lekota, a former ANC chairman, is a close ally of Thabo Mbeki, the former president of South Africa, who was forced to step down last month.
The ANC is divided between supporters of Mbeki and Jacob Zuma, who became the party's leader last year.
The upheaval in the ANC has raised concerns of a possible split in the formerly monolithic ruling party.
General elections are due in South Africa in the first half of next year.
Lekota's announcement was welcomed by the country's small opposition parties as a step towards strengthening multiparty democracy in South Africa.
However, it was met with derision by Zuma's allies in the unions and the ANC's youth wing.
|The governing party is divided between supporters of Mbeki and Zuma [AFP]
"This breakaway has nothing to do with political principle, and everything to do with the loss of political power and access to patronage,'' the South African Democratic Teachers Union said in a statement.
Responding to the rumours of a split, Zuma himself issued a warning: "Those who have grievances and other views should bear in mind that there is a limit to utilising the ANC and ANC structures to destabilise the ANC."
Lekota accused senior ANC leaders of being undemocratic, and said that consultations were under way to form a new party.
"If the leadership of the ANC continues in their arrogance ... we will proceed with the next step," he said.
Lekota said hundreds of ANC members across the country were already leaving to join established opposition parties.
He accused Zuma of "leading the ANC away from its policies".
Ebrahim Fakir, a senior researcher at the Centre for Policy Studies in Johannesburg, told Al Jazeera: "[Lekota] is now positing that there is a question of deleterious political culture taking root in the ANC, firstly.
"Secondly, that they [his supporters] are unhappy about the way in which [ex-president Thabo] Mbeki has been removed.
"And thirdly, that there have been lots of statements made by the ANC which don't seem to fit very well with what he calls the ANC's political traditions and political cultures.
"What seems to be going on is a contest for the very traditions and political cultures of the ANC within the ANC."
At Wednesday's news conference, Lekota did not refer to Zuma by name but condemned tribalism and ANC leaders who "stand on public platforms singing songs that advocate violence".
Some of Zuma's supporters celebrate his Zulu origins, while his trademark song is the apartheid-era anthem "Bring Me My Machine-Gun".
Lekota said the ANC leadership also violated the principle of equality by calling for a political solution to charges of corruption against Zuma.
ANC members must find a way "to strengthen democracy in this country", he said.
Supporters of Zuma have been accused of intimidating the judiciary during his recent legal problems.