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An unknown number of hostages are still being held by gunmen who are locked in a stand-off with security forces inside Nairobi's Westgate shopping mall.
A New Zealander is among the injured after the armed attack at the mall in the Kenyan capital Nairobi.
The Ministry of Foreign Affairs and Trade (Mfat) confirmed one New Zealander was hurt in the armed assault which killed at least 39 people and injured more than 150.
"Hostage numbers still unknown, but they are in several locations. No communication as yet. Upper levels (of the mall) have been secured,'' the Kenyan government's National Disaster Operation Centre said in a situation update posted on Twitter early on Sunday.
An AFP correspondent at the scene said operations by security forces are continuing, 17 hours after the attack began and as dawn approached in the Kenyan capital.
Somalia's al Qaeda-linked Shebab rebels have claimed responsibility for the attack.
"The work is continuing, but you cannot rush these things,'' an army officer posted on the perimeter cordon said.
"Our teams are there, we are watching and monitoring, we will finish this as soon as we can.''
The attack was reportedly carried out about 12pm yesterday by gunmen with links to al-Qaeda.
An Mfat spokesperson said the New Zealander involved was in a stable condition in hospital. No further details would be released.
"The Kenyan authorities are treating the incident as a terrorist attack and are responding accordingly,'' Mfat said.
Consular assistance was being provided by the New Zealand High Commission in Pretoria. They have also been in contact with the injured person's next of kin and are speaking with the Kenyan Foreign Ministry, the spokesperson said.
While there were 123 Kiwis registered on www.safetravel.govt.nz as being in Kenya, there had been no further information to suggest any other New Zealanders had been caught up in the attack.
Al-Shabab said on its Twitter feed that Kenyan security officials were trying to open negotiations. "There will be no negotiations whatsoever," al-Shabab tweeted.
Reports of the attack revealed terrified shoppers huddled in back hallways and prayed they would not be found by the armed gunmen, who were also lobbing grenades.
When the coast was thought to be clear, crying mothers clutching small children and blood-splattered men sprinted out of the four-story mall.
Foreigners have been confirmed among the dead. French president Francois Hollande said that two French women were killed, and there were reports of American citizens injured. However, the U.S. State Department said it had no further details.
President Kenyatta called the security operation under way "delicate'' and said a top priority was to safeguard hostages.
As night fell in Kenya's capital, two contingents of army special forces troops moved inside the mall.
Police and military surrounded the huge shopping complex as helicopters buzzed overhead. An Associated Press reporter said he saw a wounded Kenyan soldier put into an ambulance at nightfall, an indication, perhaps, of a continuing shoot-out inside.
Witnesses said at least five gunmen - including at least one woman - first attacked an outdoor cafe at Nairobi's Westgate Mall, a shiny, new shopping center that hosts Nike, Adidas and Bose stores.
The mall's ownership is Israeli, and security experts have long said the structure made an attractive terrorist target.
The attack began shortly after noon with bursts of gunfire and grenades.
Shoppers - expatriates and rich Kenyans - fled in any direction that might be safe: into back corners of stores, back service hallways and bank vaults. Over the next several hours, pockets of people poured out of the mall as undercover police moved in. Some of the wounded were moved out in shopping carts.
"We started by hearing gunshots downstairs and outside. Later we heard them come inside. We took cover. Then we saw two gunmen wearing black turbans. I saw them shoot,'' said Patrick Kuria, an employee at Artcaffe, the restaurant with shady outdoor seating.
Frank Mugungu, an off-duty army sergeant major, said he saw four male attackers and one female attacker. "One was Somali,'' he said, but the others were black, suggesting that they could have been Kenyan or another nationality.
Al-Shabab, on its Twitter feed, said that it has many times warned Kenya's government that failure to remove its forces from Somalia ``would have severe consequences.'' The group claimed that its gunmen had killed 100 people, but its assertions are often exaggerated.
"The attack at #WestgateMall is just a very tiny fraction of what Muslims in Somalia experience at the hands of Kenyan invaders,'' al-Shabab said. Another tweet said: "For long we have waged war against the Kenyans in our land, now it's time to shift the battleground and take the war to their land #Westgate."
MFAT have advised New Zealanders currently in Nairobi to be particularly security conscious.
"Follow any instructions issued by the local authorities, avoid the vicinity of the Westgate shopping mall, and keep family in New Zealand informed of their wellbeing," the spokesperson said.
New Zealanders concerned for the well-being of family in Nairobi should make direct contact with their loved ones. If they have on-going concerns, the Ministry of Foreign Affairs and Trade can be contacted on 04 439 8000.
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