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Three British nationals were killed in Saturday's attack on a shopping centre in the Kenyan capital Nairobi - and that number is likely to rise, the Foreign Office has said.
Prime Minister David Cameron called it "an absolutely sickening and despicable attack of appalling brutality".
At least 59 people were killed and 175 injured in the attack.
Between 10 and 15 attackers and an unknown number of civilians are still in the building.
The next of kin of the dead British nationals have been informed, the Foreign Office said.
The Somali militant group al-Shabab says it carried out the attack on the upmarket Westgate shopping centre in response to Kenyan military operations in Somalia.
On Sunday, Kenyan president Uhuru Kenyatta said the group of attackers was made up of both men and women.
'Don't represent Islam'
Prime Minister David Cameron condemned the attacks, adding "because the situation is ongoing we should prepare ourselves for further bad news".
"These appalling terrorist attacks that take place where the perpetrators claim they do it in the name of a religion - they don't," he said.
"They do it in the name of terror, violence and extremism and their warped view of the world. They don't represent Islam or Muslims in Britain or anywhere else in the world."
An image grab taken from AFP TV shows civilians taking cover following an attack by masked gunmen in a shopping mall in Nairobi on September 21, 2013
About 1,000 people managed to escape from the Westgate centre
Earlier on Sunday, Kenyan interior minister Joe Lenku gave an update on the numbers of those confirmed dead and injured and said 1,000 people had managed to escape from the shopping centre.
As well as British, French, Chinese, Ghanaian and Canadian citizens have also been confirmed dead.
And Kenyan president Mr Kenyatta revealed in a speech on Sunday that his own nephew and his nephew's fiancée had been killed in the attack.
Of this responsible, Mr Kenyatta said: "They shall not get away with their despicable and beastly acts.
"We will punish the masterminds swiftly and indeed very painfully."
There is now a stand-off between the Kenyan military and police and the remaining attackers.
Al-Shabab has claimed there are at least 36 hostages, but this cannot be independently confirmed. There are also likely to be people hiding away from the attackers.
The government's emergency response committee, Cobra, has met twice to discuss the attacks.
David Cameron: "We have to brace ourselves for more bad news"
The Foreign Office said a rapid deployment team had been sent from London to Nairobi to provide consular support, staff from Addis Ababa in neighbouring Ethiopia had also been sent to Nairobi and the UK High Commission in Nairobi had consular staff near the shopping centre site and at nearby hospitals.
The Labour Party conference in Brighton held a minute's silence for the three British victims.
Party leader Ed Miliband said the "terrible attack reminds us all of the continuing need for vigilance from our security services and ongoing international cooperation in the battle against terrorism".
The attack began at about 12:00 local time (09:00 GMT) on Saturday, when the militants entered the Westgate centre, throwing grenades and firing automatic weapons. A children's day was being held at the time - children are among those reported killed.
Witnesses report seeing many bodies strewn round tables of unfinished fast food - with pop music left playing in the background.
Some witnesses said the militants told Muslims to leave and said non-Muslims would be targeted.
British nationals concerned about friends or family can contact the Foreign Office on +44 (0)20 7008 0000.