Past protests have led to clashes with police and resulted in casualties.
"Kenyans are breathing a sigh of relief," Yvonne Ndege, Al Jazeera correspondent in Nairobi, reported.
She said Odinga's decision to call off the protests was "evidence perhaps that Kofi Annan is starting to get somewhere with these two parties".
Annan, who asked Odinga to call off the demonstrations, suspended month-long talks on Tuesday as both sides blamed each other for the deadlock.
Annan said he would personally appeal to the two leaders to strike a deal because talks were "turning around in circles".
But he emphasised the talks had not been abandoned and said on Wednesday that a solution could still be reached.
"Issues that divide the parties are bridgeable ... with political will," Annan said. "The solution must be found in the mediation room."
Moses Wetangula, Kenya's foriegn minister, told Al Jazeera the government had already made a large number of concession to Odinga's party.
"We have made many, many concessions to ODM [Odinga's party]," he said.
"We have agreed to set up the office of prime minister, we have agreed to set up the office of two deputy prime ministers ... We have ageed to set up a truth and reconciliation copmission. We've agreed to set up an indpendent review committee."
He also indicated the government was unhappy with how mediation efforts have been conducted.
"I've advised Kofi Annan before that when you are dealing with issues such as this you don't set deadlines, you can set targets. It's easier to hit your targets than your deadlines," said Wetangula.
In an editorial, Kenya's The Daily Nation newspaper said: "If violence breaks out and drives the country into war as a result of the failure [of the negotiations], the blood of its victims will be on the hands of the politicians who made it impossible for Dr Annan to reunite Kenya."
Jakaya Kikwete, Tanzania's president and chairman of the African Union, arrived in Nairobi on Wednesday to bolster international efforts for a deal.
Kikwete is scheduled to meet Kibaki and Odinga during his visit.
On Tuesday Condoleezza Rice, the US secretary of state, criticised Kibaki and Odinga for failing to end their political standoff and said Washington would take "necessary steps" if a solution was not found.
The country remains on edge with fears that fresh bouts of tribal fighting could break out.
Violence has also forced at least 600,000 people from their homes, mainly in the capital's slums and western region, regarded as the country's breadbasket.