Central Nairobi was quieter on Sunday after riots in the days after the election results were announced. (Photo: Xinhua)

Kenya's defeated opposition faced mounting calls at home and abroad to calm their supporters Sunday after claims of election rigging sparked violent protests that left at least 11 people dead.

Odinga's flashpoint strongholds in western Kisumu and Nairobi's slums were quiet Sunday, with signs life was returning to normal after two days of running battles with police. Officers in some clashes used live ammunition to disperse stone-throwing, tyre-burning residents, with tear gas also fired.

UN secretary general Antonio Guterres urged thwarted presidential candidate Raila Odinga to "send a clear message to his supporters urging them to refrain from violence", a message echoed by British Foreign Secretary Boris Johnson.

The anger erupted on Friday night after President Uhuru Kenyatta was declared the victor by a large margin against his rival Odinga following an election pollsters had described as too close to call.

Odinga's National Super Alliance (Nasa) coalition has insisted their candidate is the rightful winner, saying he was robbed of victory through hacking and manipulation of an electronic vote tallying system.

However calls for them to take their grievances to court, while Kenya's foreign partners heap congratulations on Kenyatta, have left them isolated and under mounting pressure.

Odinga (72), a mainstay of the Kenyan opposition since the 1980s, has been silent since his loss was announced, but his party officials have said they will neither back down nor take their grievances to court.

"We will not be cowed, we will not relent," Nasa official Johnson Muthama said on Saturday.

In Nairobi's Mathare slum, shops and markets slowly began opening and there was no sign of police or protesters Sunday morning.

"We want to hear Raila. We want to hear what he has to say. It's him who will guide us. If he tells us to go on the streets, we will go on the streets. If he wants us to stay home, we will stay stay home," said 25-year-old hairdresser Humpfrey Songole in Mathare.

Doctors without Borders (MSF) said on Twitter it had treated 54 wounded people in its clinics.

The post-election violence is the worst since a disputed 2007 poll which Odinga claimed was stolen from him. That led to two months of protests and ethnic killings which left 1 100 dead and 600 000 displaced.

Britain's Johnson urged Kenya's opposition to "exercise restraint" to ensure calm.

The European Union's foreign affairs chief Federica Mogherini urged the opposition "to respect the results and to use legal means available for appeals and complaints."

Odinga, who lost his fourth shot at the presidency, in 2013 also disputed Kenyatta's poll victory. He took his case to the Supreme Court where he lost. "We have been there before. Court is not an alternative," said top Nasa official James Orengo.

Kenyan media also urged Odinga to step up and address his supporters.

Interior Minister Fred Matiangi denied there had been any casualties or that "innocent protesters" had been killed, saying police had clamped down on "criminal elements" taking advantage of the tension to loot and rob.