"If the IGAD meeting goes on in spite of our call for it not to go on," said Anyang Nyongo, secretary-general of the opposition Orange Democratic Movement (ODM), "we shall call upon Kenyans to come out in their big numbers for a peaceful demonstration in Nairobi to strongly protest."
The government has banned street protests, and earlier ones have led to looting, rioting and a crackdown by police.
'Provocative statements'
Kofi Annan, the former UN secretary-general mediating talks between the two sides, rebuked the opposition for the threat.
"We have a demand that the parties avoid provocative statements outside negotiations," Annan told reporters.
"We are going to be vigilant on that. I think there is a clear understanding that it should not have been done and there will be no mass protests."
On Tuesday, Annan pushed the two sides to focus on "the political crisis arising from the disputed presidential electoral results".
Annan began his mission in Kenya after Raila Odinga, the opposition leader insisted on external mediation.
Odinga says Mwai Kibaki, the Kenyan president returned to power in disputed elections in December, was illegally won his reelection through vote-rigging.
Fresh violence
Of the 12 people killed in violence on Tuesday, nine were shot by police cracking down on gangs of youths who have attacked houses and other property, police sources said.
The death toll from the post-election violence grew to over 1,000 victims, according to the Red Cross, with 300,000 people displaced since elections in December returned Mwai Kibaki, the Kenyan president, to power.
The opposition has refused to recognise Kibaki's victory, claiming widespread rigging. International observers have also cited serious flaws during vote-counting.
Investigation into abuses
UN human rights investigators headed to Kenya to conduct a three-week investigation into alleged violations committed since the elections, a UN spokesman said on Tuesday.
The team of seven will interview officials, survivors of ethnic violence and the relatives of victims, and report to Louise Arbour, the UN High Commissioner for human rights.
The team is due to arrive in Nairobi on Wednesday.
Annan's efforts to mediate between the two side suffered a set back on Monday when Cyril Ramaphosa, a South African negotiator who he had asked to help mediate the talks, pulled out of mediation efforts amid claims by Kibaki's allied that he was biased.
The South African government angrily rejected those claims.
Aziz Pahad, South Africa's deputy foreign minister, said Ramaphosa had a proven record as a trouble-shooter and could have played a valuable role in bringing an end to post-election violence.
"The role played by Ramaphosa during the South African democratic process, as well as his contribution to the Irish peace process, has indicated his ability to seek solutions in the interests of peace and democracy and without taking sides," Pahad said.
The millionaire businessman denied he had business dealings with Odinga but acknowledged he had failed to win the trust of both sides.