Officials said almost all hostages had been rescued and nearly the entire Westgate shopping mall was under control by Monday night, Xinhua reported.
Police Inspector General David Kimaiyo said Monday that security forces were trying to gain access from the rooftop of the upscale Westgate mall.
"Thumbs up to our multi-agency team. We have just managed to rescue some hostages. We are increasingly gaining advantage of the attackers," Kimaiyo said via his Twitter account.
Kenya also claimed to have killed two of the 10 to 15 terrorists of the Somali-based Al Shabab.
Thick, black smoke was still billowing up from the mall building hours after explosions and heavy gunfire were heard in an operation to free hostages Monday.
The standoff between Kenyan security forces and attackers from Al Shabab lasted for more than 50 hours since they launched an attack on the luxurious mall at around 10:30 a.m. (7.30 a.m. GMT) Saturday, when large numbers of foreign visitors and local people were shopping.
Sixty-two people have been confirmed dead and 175 others injured.
The Al-Shabaab has claimed responsibility for the attack, saying it was revenge for a Kenyan cross-border attack in Somalia in October 2011.
The group said the message sent to the Kenyan government and public "is and has always been just one: remove all your forces from our country".
Kenya beefed up security along its borders with Ethiopia and Somalia to prevent insurgents from entering the country.
Joseph Ole Lenku, Kenya’s cabinet secretary in charge of internal security, said Monday that the security apparatus in the country has been ordered to ensure that no one gets in or out of the country.
All major hotels, restaurants, bars and public service vehicle operators across the country have been directed to enhance security by reviewing their security arrangements which include screening visitors.
The Kenyan government said Monday that it was holding "some individuals" for questioning at Kenya's major airport.
Principal Secretary in the Interior Ministry Mutue Iringo said the individuals, whose identities were not disclosed, were arrested at Jomo Kenyatta International Airport en route to Turkey.
"We ask all officers dealing with vital identification documents to be very careful," Iringo said after the arrests.
Among the dead in the mall attack were visitors from Canada, France, Britain, South Africa, China, India, the Netherlands and the US.
In New Delhi, officials named two of the Indians killed as Sridhar Natarajan, 40, from Tamil Nadu and an employee of a local pharmaceutical firm Harley's Limited; and Paramshu Jain, eight, the son of Manoj Jain, the branch manager of Industrial Area Branch, Bank of Baroda (Kenya Limited).
Top leaders of the European Union Monday condemned the terror attack.
"It was with great shock and sadness that we learnt of the brutal attack on innocent citizens at the Westgate Shopping Centre in Nairobi Saturday. The European Union firmly condemns all such terror attacks," said President of the European Council Herman Van Rompuy and President of the European Commission Jose Manuel Barroso in a joint message to Kenyan President Uhuru Kenyatta.
They said that such acts should not be allowed to weaken their common resolve to eliminate the scourge of terrorism from East Africa and to prevent such attacks in the future.
US President Barack Obama Monday called the attack a "terrible outrage" and said that his country stood with Kenya.
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