Kenyan security forces were locked in a standoff on Sunday with gunmen who killed at least 39 people in an assault at an upmarket shopping mall in Nairobi, where the Al Qaeda-linked militants were holding an unknown number of hostages.
The Somali Islamist group al Shabaab claimed responsibility for Saturday's attack on the Kenyan capital's Westgate mall, which is frequented by Westerners as well as Kenyans.
Several foreigners, including a Canadian diplomat, were among the dead.
Kenyan President Uhuru Kenyatta said more than 39 people had been killed, among them close members of his own family.
A senior government official said on his Twitter feed that more than 300 people had been wounded.
The dead included children, and the wounded ranged in age from 2 to 78.
France said two of its citizens had been killed, and Canada said two Canadians had died, including a 29-year-old diplomat.
US Secretary of State John Kerry said there were no Americans among the dead but that several US citizens had been hurt and the wife of a US diplomat working for the US Agency for International Development was killed.
Police said the attackers were holding an unknown number of people on Sunday and the standoff was focused on the mall's Nakumatt supermarket, one of Kenya's biggest chains.
Kenyatta said the security forces were engaged in a "delicate operation," with the top priority being to safeguard the lives of people being held.
Al Shabaab, which has links to Al Qaeda and is battling Kenyan and other African peacekeepers in Somalia, had repeatedly threatened attacks on Kenyan soil if Nairobi did not pull its troops out of the Horn of Africa country.
The group appeared to taunt the security forces, saying on its official Twitter handle @HSM_Press that there would be no negotiations whatsoever with Kenyan officials over the standoff.
"10 hours have passed and the Mujahideen are still strong inside #Westgate Mall and still holding their ground. All praise is due to Allah!", the group said.
The raid presents Kenyatta with his first major security challenge since a March election victory.
He has vowed to defeat the militants who have said it is time to shift the war to Kenyan soil.
"We have overcome terrorist attacks before," he said.
The assault has been 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.
In 2002, the same militant cell attacked an Israeli-owned hotel on the coast and tried to shoot down an Israeli jet in a coordinated attack.
Kerry said the United States had offered assistance to the Kenyan government.
"The perpetrators of this heinous act must be brought to justice, and we have offered our full support to the Kenyan Government to do so," he said in his statement.
Relatives of hostages thought still to be trapped inside the mall were keeping vigil in a nearby Hindu centre, waiting for the next move by the security forces.
Kevin Jamal said his sister was taken hostage while shopping at the mall, and he had been waiting for more than six hours.
"I want her to come out alive," Jamal told Reuters as he joined Kenya Red Cross Society volunteers for a meal of hot curry and chips served by the centre.
He said the Kenyan security agencies could have done better, saying, "They should not allow themselves to be outmanoeuvred by less than 20 people."
Police said it was not clear how many attackers they were dealing with, and those rescued said at least one of the attackers was a woman.
One of the attackers had been shot and arrested, but died shortly afterwards at a hospital.
A fierce gun battle erupted between the police and the militants after Saturday's initial assault.
The shooting continued hours after the first attack and soldiers then managed to enter the building, hunting for the attackers shop by shop.
Witnesses said the attackers were armed with AK-47 rifles and wore ammunition belts.
Police said the attack occurred during a children's cooking competition hosted by a radio station at the mall, just as the winners were about to receive prizes.
There was a lull in activity in the hours after midnight.
Troops were milling around at the mall, near two armoured personnel carriers and two big fire trucks, one with a long, extendable ladder.
Music was still playing and a video screen was on at a gourmet burger shop.
Journalists and curious bystanders were moved out of the mall onto a side road.
Kenya sent its troops into Somalia in October 2011 to pursue the militants it blamed for kidnapping tourists and attacking its security forces.
The major attack on a mall that draws tourists, expatriates and Kenya's wealthy elite risks hammering an already struggling tourism sector in Kenya and could puncture Kenyatta's plans to boost East Africa's biggest economy's reputation as a sound investment destination.
Al Shabaab's last big attack outside Somalia was a twin attack in neighbouring Uganda, targeting people watching the World Cup final on television in Kampala in June 2010.
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