"Kenyans are entitled to protest peacefully at this blatant violation of their fundamental rights," Anyang Nyongo, secretary-general of the ODM, said.
He also demanded international sanctions against the government, saying: "You cannot trust a government that steals votes with the precious resources we get from our international partners.
"It's inappropriate to trust this government with a single cent."
Responding to the calls for mass protests, Major General Mohamed Hussein Ali, the police commissioner, said: "We have ... the options, in the interest of security, to cancel such meetings, demonstrations or rallies if we think they are going to contravene peace and security.
"Police think it is not appropriate at this time."
Tear gas, water cannons and live bullets fired have been used to block previous attempts to assemble.
John Kufuor, chairman of the African Union and president of Ghana, left Nairobi on Thursday night after two days of mediation failed to persuade Kibaki and Odinga even to meet each other.
Kofi Annan, the former UN secretary-general, has agreed to take over mediation efforts but is not expected to arrive in Nairobi before Tuesday, according to his office in Geneva.
The two sides have traded blame for the continuing political deadlock.
According to the government, Kibaki "offered dialogue," but Odinga was not responsive. Odinga said Kibaki refused to sign an agreement to establish an interim coalition government and conduct an inquiry into the Electoral Commission of Kenya.
A government spokesman acknowledged Kibaki had not signed, saying he was not involved in the consultations.
Odinga has said he would meet Kibaki only in the presence of an international mediator. Kibaki wants direct talks.
On Friday, Kibaki reiterated "his commitment to dialogue in the search for a lasting solution to the current political situation in the country", his office said in a statement.
In a meeting with religious leaders, the president "said he was ready to work with other leaders in ensuring that peace is restored in all parts of the country".
Several nations, including the United States and Britain, Kenya's former colonial ruler, have expressed displeasure at irregularities in the presidential vote count, and are pressing for some sort of power-sharing agreement.
But hopes for a compromise were dampened when Kibaki's allies were sworn in on Thursday as cabinet ministers.
The unrest has tarnished Kenya's democratic credentials, damaged east Africa's largest and previously booming economy, hit supplies to neighbours, and unnerved Western donors.
The United Nations estimated on Friday that 500,000 people caught up in post-election violence in Kenya will need humanitarian assistance, including vital food rations.
It plans to seek funds next week to help more than a quarter of a million Kenyans forced to flee their homes, but said its appeal to donors could be expanded.
Elisabeth Byrs, spokeswoman of the UN Office for the Co-ordination of Humanitarian Affairs (OCHA), told a news briefing in Geneva: "We fear malnutrition will rapidly worsen if insecurity and the lack of access to food and assistance persists."
The UN World Food Programme (WFP) has distributed food for 33,000 people in Nairobi's slums, where many residents have lost their jobs and goods are scarce, a spokeswoman said.
Nearly one in three Kenyan children under five were already suffering severe malnutrition before the crisis, the UN Children's Fund (Unicef) said.
Unicef has distributed 11,000 family kits with tarpaulins, blankets and soap in Eldoret in the Rift Valley, which has been worst hit by violence.