The police had tightened security ahead of the planned rallies
Raila Odinga said he hoped international mediation could solve the crisis. He says the vote was rigged in favour of President Mwai Kibaki.
The top US official for Africa, Jendayi Frazer, has said Kenyans have been "cheated" by their political leaders.
The police now say that 600 people have died in election violence - up from the previous official figure of 350.
Some 250,000 people have fled their homes in clashes between rival political supporters, ethnic groups and the police.
We have at least 600 dead... some bodies are still in the bushes where fighting occurred
Senior police officer
Q&A;: Poll violence
After a week of clashes, some shops and businesses have re-opened in the capital, Nairobi and "matatu" mini-bus taxis have returned to the streets after several days when the city was deserted.
"We are now assured that the mediation process is about to start," Mr Odinga said after meeting Ms Frazer.
"We are therefore informing our supporters countrywide that there will be no public rallies [on Tuesday]."
Roads blocked
Mr Odinga said Kenya was living through the gravest crisis it had faced and condemned the violence that had taken place.
Ms Frazer said there may have been vote-rigging by both sides and that ordinary Kenyans had been let down.
Charities are warning of a looming health crisis
"The only way to restore the Kenyan people's rights and confidence in the system is that the political leaders have to stop the violence, because innocent people are dying."
Meanwhile, Mr Kibaki has reconvened parliament for 15 January.
Mr Odinga's Orange Democratic Movement won a majority in parliament but does not have the two-thirds needed for a vote of no-confidence in the president.
Both sides have accused the other of ethnic cleansing during a week of violence after Mr Kibaki was declared the winner.
HAVE YOUR SAY The country-wide violence has affected virtually every Kenyan
Geoffrey Mwango, Mombasa
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"We have at least 600 dead... some bodies are still in the bushes where fighting occurred."
Mr Odinga said he understood that Ghana's President John Kufuor, current chairman of the African Union, would also be going to Kenya soon for talks.
Last week, the government said there was no need for Mr Kufuor to go to Kenya.
Many in need
Mr Kibaki has offered to form a "government of national unity" but Mr Odinga says the president must step down.
The BBC's Peter Greste says there is no sign of this and there remains a large gap between the two sides' positions.
The government says it has deployed its military engineering unit to assist in unblocking the main highways to enable relief supplies to be delivered to displaced people, and for public transport to resume.
The head of the humanitarian services committee, Rachael Arunga, told a news conference in Nairobi that sufficient supplies were yet to reach thousands of displaced people in urgent need.
Ms Arunga said the Rift Valley province was the worst hit area and efforts were being made to deliver food items, tents and medicine to the displaced people.
Seven people were killed in a shoot-out at a police station on Sunday and there have been further clashes in Mombasa.
European Union observers have criticised the way some of the votes were counted, including anomalies between the results announced locally and nationally.
Ghana’s President  is expected to travel to Kenya this week to help resolve the escalating violence that has plunged Kenya into a political crisis. This comes after Kenyan President Mwai Kibaki sent an envoy to brief the Ghanaian president, who is also chairman of the African Union on the current situation in Kenya. Kibaki has also reportedly said he is willing to dialogue without pre-condition with opposition leader  of the  who is claiming he won . Odigna has decided to call off protests that were due to take place tomorrow as a result of the action. He has agreed to take part in the  mediation process. This is despite earlier reports that he would not take part in the mediation.

 is Ghana’s foreign minister. He tells ''VOA'' reporter Peter Clottey that President Kufuor is concerned about the tensions in Kenya.

“Basically, the president has been invited to Kenya to see for himself the situation and offer advise as to how the two leaders can come together to stop what is happening in Kenya. As you know, people are being killed and there are a lot of disturbances in Kenya and Kenya is like a pillar of a democratic country is now blowing up in our faces. And I don’t think it is for any African country to stand by and more so the chair of the AU (Africa Union) to sit by for such a thing to happen to Kenya. He (president Kufuor) is going there to offer advice,” Osei-Adjei noted.

He reckoned that President Kufuor’s expected trip would yield positive results that would help alleviate the escalating violence in Kenya.

“We hope so. He (President Kufuor) wouldn’t move from Ghana to Kenya not expecting to make a difference to make the situation calm and normal. You know so that is what we expect,” he said.

Osei-Adjei denied speculations that President Kufuor’s mediation efforts could possibly worsen the situation just like in Zimbabwe.

“No, I don’t think so. Zimbabwe is quite a different issue. This is coming out as a result of elections, the recent elections and what is happening that we have to be there to ensure that the two leaders can sit down and then calm the situation,” Osei-Adjei pointed out.

He said President Kibaki invited the Ghanaian president to help solve the escalating violence, which is blamed on the controversy surrounding the December elections.

“Well, the envoy came yesterday to brief the president of Ghana and at the same time the chair of the AU the situation before elections, during elections and after the elections. Upon this then he also added the President (Kibaki) has also asked him to invite the president of Ghana that is President Kufuor of Ghana to be there to help calm the situation. This is what was said yesterday that President Kufuor is going to Kenya to talk to the two leadership and then make them come to if you like some the peace pipe so that things in Kenya will calm down so that of course the necessary things could be done, and then ensure that people go about their normal businesses,” he said.