Fresh gunfire erupts at hostage crisis in Nairobi shopping mall
* After quiet night, gunfire and blasts around dawn
* Unclear how many hostages being held, death toll so far 68
* Somali Islamists linked to al Qaeda claims responsibility
* Group wants withdrawal of Kenyan troops from Somalia
Journalists near the upmarket Westgate complex heard sporadic shots and also heavy bursts of rifle fire and muffled blasts on at least two occasions after daybreak.
About 10 and 15 attackers - thought to be militants from the Somali al-Shabab movement - are still inside the Westgate shopping centre.
An al Shabaab spokesman warned that the Islamists would kill hostages if Kenyan security forces, who are being assisted by Western and Israeli experts, tried to storm their position:
"Israelis and Kenyan forces have tried to enter Westgate by force but they could not," Sheikh Ali Mohamud Rage said in an audio statement posted online. "The mujahideen will kill the hostages if the enemies use force."
Security forces had secured most of the complex yesterday, freeing many people who had hidden in terror. Though they hoped for a quick solution, rescuing those held will be difficult.
Survivors' tales of Saturday's military-style, lunchtime assault by squads of attackers hurling grenades and spraying automatic fire, has left little doubt the hostage-takers are willing to kill. Previous such raids around the world suggest they may also be ready to die with their captives.
In Somalia, Kenya's northern neighbour devastated by two decades of civil war, al Shabaab have demanded President Uhuru Kenyatta pull out Kenyan troops, who have pushed the militants on to the defensive over the past two years as part of an African Union-backed peacekeeping mission. Kenyatta refused.
It was unclear how many may be held hostage. Colonel Cyrus Oguna, a Kenyan military spokesman, said that most of those freed in a search and rescue operation yesterday had not been held by the gunmen but had found places of refuge. He said "a very small number" were still captive, but gave no detail.
"We will not negotiate with terrorists," he added.
Asked at a news conference yesterday about whether captives had been wired with explosives, Kenyatta declined comment.
The president, who lost a nephew in Saturday's killing, vowed to hold firm in the "war on terror" in Somalia and said, cautiously, that Kenyan forces could end the siege.
"I assure Kenyans that we have as good a chance to successfully neutralise the terrorists as we can hope for," he said. "We will punish the masterminds swiftly and painfully."
A military spokesman for al Shabaab said his group had nothing to fear. "Where will Uhuru Kenyatta get the power with which he threatened us?" said Sheikh Abdiasis Abu Musab.
It was unclear who the assailants were. Al Shabaab - the name means "The Lads" in Arabic - has thousands of Somali fighters but has also attracted foreigners to fight Western and African Union efforts to establish a stable government.
A London man, Jermaine Grant, faces trial in Kenya for possession of explosives. Police suspect an al Shabaab plot to attack restaurants and hotels used by Westerners and have been hunting for an Irish-born woman, Samantha Lewthwaite, the widow of a suicide bomber who took part in the London 7/7 attacks of 2005.
Some British newspapers speculated on the role the "White Widow" might have played at Westgate. The term "black widow" has been used by Chechen militants in Russia for women taking part in bombings and assaults after the deaths of their husbands.
With the stocks of a major supermarket at their disposal - the Nakumatt store is part of one of Kenya's biggest chains - the gunmen could be in a position to hold on for a long time.
British Prime Minister David Cameron, confirming that at least three Britons were already among the dead, said: "We should prepare ourselves for further bad news."
US President Barack Obama called Kenyatta to offer condolences and support. Israel, whose citizens own stores in the Israeli-built mall and have been targeted by Islamists in Kenya before, said Israeli experts were also helping.
Foreigners, including a French mother and daughter, and two diplomats, from Canada and Ghana, were killed. Ghanaian Kofi Awoonor was a renowned poet. Other victims came from China and the Netherlands. Five Americans were wounded.
Kenya's president, son of post-colonial leader Jomo Kenyatta, is facing his first major security challenge since being elected in March.
The assault was the biggest single attack in Kenya since al Qaeda's East Africa cell bombed the US Embassy in Nairobi in 1998, killing more than 200 people.
Judges at the International Criminal Court adjourned the trial of Kenyan Vice President William Ruto for a week, granting his request to return home to help deal with the crisis.
He and Kenyatta face charges of crimes against humanity for their alleged role in coordinating deadly violence after the contested 2007 elections, when they ran in rival camps. Both deny the charges. They won a vote on the same ticket in March.
Al Shabaab's siege underlined its ability to cause major disruptions with relatively limited resources, even after Kenyan and other African troops drove it from Somali cities.
"While the group has grown considerably weaker in terms of being able to wage a conventional war, it is now ever more capable of carrying out asymmetric warfare," said Abdi Aynte, director of Mogadishu's Heritage Institute of Policy Studies.
After emerging on Sunday morning from a hiding place under a vehicle in the basement car park, a woman, giving her name as Cecilia, told Reuters she had seen three of the attackers.
"They were shooting from the exit ramp, shooting everywhere," she said. "I saw people being shot all around me, some with blood pouring from bad wounds. I was just praying, praying 'God, keep me alive' and that my day hadn't come."
Witnesses said the attackers had AK-47 rifles and wore ammunition belts. One militant was shot and arrested early on in the siege, but died shortly afterwards.
For hours after the attack, the dead were strewn around tables of unfinished meals. At one burger restaurant, a man and woman lay in a final embrace, until their bodies were removed.
Kenya sent troops into Somalia in October 2011 to pursue militants whom it accused of kidnapping tourists and attacking its security forces.
Al Shabaab's last big attack outside Somalia was a double bombing in Uganda, targeting people watching the World Cup final on television in Kampala in 2010, killing 77 people.