NAIROBI, Kenya (CNN) -- Kenya's opposition leader Wednesday called off mass demonstrations that his supporters had threatened to hold the next day.
Raila Odinga had warned of "mass action" to protest the lack of progress in negotiations meant to resolve a political impasse with President Mwai Kibaki and his supporters.
Odinga and Kibaki have been at odds since facing off in a December 27 election that international monitors describe as flawed. Kibaki claimed victory and took the oath of office despite reported irregularities. Violence that followed has killed at least 1,000 and displaced 300,000.
Former U.N. Secretary-General Kofi Annan has been overseeing talks between the two sides meant to bridge the divide, but he suspended those talks on Tuesday.
On Wednesday, Odinga told reporters that his supporters would not take to the streets -- for now -- in the kind of mass action that has previously led to violence.
"We will delay mass action until further notice," he said.
Annan is meeting privately with Kibaki and Odinga.
"It is a crisis situation that we are trying to manage, and we need to understand the urgency and the need for speed," Annan said Tuesday. "I trust the two leaders understand this and will work with me expeditiously to resolve the crisis the country is in. Time is of the essence."
Earlier Tuesday, U.S. Secretary of State Condoleezza Rice said she is "disappointed" over the stalemate in power-sharing negotiations between rival Kenyan political parties and called for no further violence.
"There can be no excuse for further delay," she said in a written statement. "There can also be no excuse for violence, and those responsible must be held accountable."
The government negotiating team confirmed that it had lodged a complaint objecting to the suspension, saying progress was being made.
"It is true tempers flared in the afternoon over certain issues, but this is normal in negotiations," said negotiator Mutula Kilonzo. "We are not unintelligent and we also felt that we were being pushed, pushed and pushed, which is not fair."
The opposition party blamed Kibaki for the breakdown in talks.
"We always knew that the government plan was to drag this out for long enough in the belief that Kenyans would allow the stolen election to stand," said opposition spokesman Salim Lone.
Kibaki's win in the December voting was immediately called into question with election observers from the European Union saying they doubted the legitimacy of the count. Analysts said it was probable that both of the main parties had been involved in electoral fraud.
The fighting that followed the vote broke down along tribal lines. Members of Kibaki's Kikuyu tribe and the Luos, the tribe of Odinga, have been in the middle of the ethnic clashes.
The opposition party had said it would embark on a "mass civil disobedience campaign" if its demands aren't met in negotiations. Last month, such anti-government demonstrations turned violent, prompting police to use tear gas to disburse protesters.
More than 270,000 displaced Kenyans remain in 200 camps; 12,000 others are being looked after in Ugandan camps and estimated half million overall are in need of emergency shelter, water, food and medical care, according to John Holmes, U.N. under-secretary-general for humanitarian affairs, who briefed the U.N. Security Council on Monday.
Holmes visited the region earlier this month.
"Common threads among all the displaced groups were their urgent need for safety and security, particularly for women and children, with some disturbing accounts of continuing abuses in and around camps," he said in a written statement.
"I heard dreadful stories of murder, of rape and burning," he added. "The ethnic basis of much of what happened was tragically clear."
The implications of the violence are significant because of Kenya's long-standing role as east Africa's main transport hub. That means the fighting could disrupt the aid and humanitarian efforts coming into a wide area. E-mail to a friend
CNN's David McKenzie in Nairobi, and Zain Verjee and Elise Labott in Washington contributed to this report.