"We believe all hostages have been released," the Kenya National Disaster Operation Center said in a Twitter message.
Kenya Defence Forces (KDF) tweeted that it continued "to neutralise terrorist threat, troops now in mop-up operations in the building".
"We're in control of #Westgate," said the interior ministry.
President Uhuru Kenyatta, whose nephew and his fiancee were killed in the attack, is expected to address the nation in what is believed will be a detailed report that the terrorists have been subdued, Kenyan media reported.
Much of the hours leading to Tuesday morning were quiet as emergency services waited outside the Westgate mall in fire tenders and ambulances, with many Kenyans remaining active on social media platforms waiting for the victory signal from the security forces.
At least 62 people were killed and over 170 left injured in the assault at the mall that began Saturday after 10-15 militants of Somalia-based Al Shabab group stormed the mall.
Six more terrorists were killed Tuesday, Xinhua reported citing Kenya's Citizen TV.
The KDF had said Monday that three terrorists have been killed.
In New Delhi, the external affairs ministry Tuesday said another Indian, Sudharshan B. Nagaraj from Bangalore, was among those killed. This raises to three the number of Indians killed in the attack.
"The toll of Indian citizens killed in Westgate attack rises. Sudharshan B. Nagaraj from Bangalore sadly identified as among those killed. He was in the book trade and had only come to Nairobi on Sep 20," said the ministry.
The Indian high commission in Nairobi, it said, was in touch with Nagaraj's next of kin and associates to repatriate his mortal remains.
Earlier, Sridhar Natarajan, 40, from Tamil Nadu, and Paramshu Jain, eight, the son of a Bank of Baroda's Nairobi branch manager, were identified as among those killed by Islamist Al Shabab militants.
Kenya has long been a terrorist target. In 1998, the Al Qaeda had bombed the US embassies in Nairobi and Dar-es-Salaam, Tanzania, killing 224 people and injuring hundreds more.
In 2002, militants bombed an Israeli-owned luxury hotel near Mombasa, killing 13 people, and also tried to shoot down an Israeli airliner.
Kenya's decision in October 2011 to get directly involved in military operations in Somalia against Al Shabaab increased the chances of a reprisal act of terror by its supporters and heightened the threat.
Neighbouring Uganda has also been targeted, and at least 74 people were killed in twin bomb attacks by Al Shabaab in Kampala in 2010. Militants have also attacked religious gatherings in Tanzania and there have been a spate of acid attacks in Zanzibar.
--IANS (Posted on 24-09-2013)