Five attackers were shot dead by troops and 11 suspects are in custody, Kenyatta said in a televised address to the nation, reported BBC. He declared three-day national mourning starting from Wednesday.
"Fellow Kenyans, we have been badly hurt and feel great pain and loss, but we have been brave, united and strong. Kenya has stared down great evil and triumphed," he said.
The president also informed that three floors of the Westgate shopping centre had collapsed during the "tail end" of the operation and there were still at least three bodies in the rubble.
Kenya has "shamed and defeated our attackers" but the "losses are immense", he said while admitting the death of 61 civilians and six soldiers in the operation.
Stating that several bodies, lying under rubble from collapsed parts of the building were yet to be recovered, the Kenyan president added some 62 others people were hospitalised. Many others were being treated for shock and are undergoing counselling.
Assuring the public a thorough investigation of the siege, Kenyatta said: "I promise that we shall have a full accountability for the mindless destruction, deaths, pain, loss and suffering we have all undergone as a national family.
"These cowards will meet justice, as will their accomplices and patrons, wherever they are."
On reports of British and US nationals' involvement in the incident, Kenyatta said he could not confirm reports that a British national and two or three US citizens were involved in the attacks.
He, however, said forensic experts were carrying out tests to ascertain their nationalities.
The dead also included three Indians.
Sudharshan B. Nagaraj from Bangalore, was Tuesday identified among the dead. "He was in the book trade and had only come to Nairobi on Sep 20," an Indian External Affairs ministry statement said.
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 in the Islamist militants' terror strike in the Westgate mall.
Meanwhile, Scotland Yard in London confirmed that a team of officers has travelled to Nairobi to help with "post incident procedures" including gathering scientific evidence as well as supporting the work of British coroners.
Militants stormed the Westgate centre last Saturday, throwing grenades and firing on shoppers and staff. Islamist group al-Shabab later claimed the responsibility, stating that it carried out the attack in retaliation for Kenyan army operations in Somalia.