Kenyan forces have brought more people out overnight from the shopping mall where Islamist militants are holding hostages, and troops are "closing in" on the attackers, the police inspector general, David Kimaiyo, said on Monday, the third day of the siege.
He said Kenyan security forces had "rescued more hostages" but made no mention in his Twitter comment about engaging with the militants. Several people in the past two days have emerged after hiding rather than being held at gunpoint.
Kenyan officials have said they have isolated the attackers in the mall, and since last night have suggested that the operation was in its final stages.
Gunfire and explosions sounded earlier on Monday from the Nairobi shopping mall where militants from Somalia's al Qaeda-linked al Shabaab movement were holding hostages into a third day after killing more than 60 people.
As day broke, following a quiet night, Reuters journalists near the upmarket Westgate complex heard bursts of rifle fire and muffled blasts. A Kenyan Red Cross official, Abbas Guled, said there appeared to be clashes inside the building.
But there was no indication of the fate of people whom the authorities had said on Sunday were being held by 10 to 15 gunmen - and possibly women - inside a large supermarket.
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, a spokesman for al Shabaab said President Uhuru Kenyatta must 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, told Reuters that most of those freed in a search and rescue operation on Sunday 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.
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Asked at a news conference on Sunday 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 told Reuters 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.
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."
U.S. 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 U.S. Embassy in Nairobi in 1998, killing more than 200 people.
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.
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"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 twin assault in nearby Uganda, targeting people watching the World Cup final on television in Kampala in 2010, killing 77 people.