In a televised address Tuesday, Kenyatta said losses in the four-day attack at the Westgate Premier Shopping Mall were "immense" and 11 suspected Islamist militants were in custody, the BBC reported.
The Somali Islamist organization al-Shabaab claimed responsibility for the siege, which began Saturday, saying it was retribution for Kenya's decision to send thousands of troops to help the neighboring Somali government fight al-Shabaab insurgents two years ago.
"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," he said.
"These cowards will meet justice, as will their accomplices and patrons, wherever they are."
Kenyatta said the bodies of several victims remained unrecovered beneath rubble at the shopping center. He declared a three-day period of national mourning, beginning Wednesday.
About 175 people were injured in the attack, 62 of whom were still hospitalized Tuesday, the BBC said.
The dead include at 18 non-Kenyans, including six Britons. Kenyatta said forensics tests would determine whether the attack force included a British national and at least two U.S. citizens, as some reports have said.
Kenya Defense Forces spokesman Cyrus Oguna said military personnel were still mopping up inside the mall, even as explosions and gunfire were being reported.
"The delicate and complex nature of the Westgate Mall siege rescue operation called for extreme care and caution to ensure the safety and security of the hostages," Oguna told the Standard Digital.
Karangi said "such cowardly acts of terrorism will not dampen KDF resolve to ensure that peace and stability is regained in Somalia and in the region."
Police said vehicles abandoned at a parking lot near the Westgate Mall have been cleared for owners to pick up, provided they have proper proof of ownership, the Daily Nation reported.
Inspector General of Police David Kimaiyo noted, however, it would take more time for police to begin allowing vehicles parked at the mall to be removed.
"We are yet to finish with Westgate because specialized teams from police will move in once the mall has been cleared by those freeing the hostages," he said.
At The Hague, Netherlands, the International Criminal Court prosecutor's office said it was prepared to work with Kenya in bringing the Westgate Mall attackers to justice.
"In expressing her solidarity with the victims, their families and the people of Kenya, and with full respect for the primacy of jurisdiction of the Republic of Kenya, the prosecutor [Fatou Bensouda] stands ready to work with the international community and the government of Kenya to ensure that those responsible for these crimes are brought to justice," the statement issued Tuesday said.
Kenyan Foreign Minister Amina Mohamed told PBS some of the attackers were from the United States.
"As you know, both the victims and the perpetrators came from Kenya, the United Kingdom and the United States," Mohamed said. "From the information that we have, two or three Americans, and I think so far I've heard of one Brit," are among the attackers.
State Department and White House officials said the United States doesn't have any confirmation of Americans having been involved in the attack.
Intelligence analysts were closely examining electronic intercepts to try to verify the militants' claims, law enforcement officials told CNN.
Somali leaders in Minnesota worked to distance their community from the attacks.
"The safety and security of the United States is of utmost importance to Somali-Americans, and we are committed to be in the forefront of defeating extremism," Abdisalam Adam, an imam of the Islamic Civic Society of America, was quoted in the Minneapolis Star Tribune as telling a news conference with other Somali religious leaders Monday.
"This kind of activity, killing innocent people, has no base or any relationship with Islam," said Abdirizak Hashi, an imam at Abubakar As-Saddique Islamic Center in Minneapolis.
U.S. President Barack Obama said Monday the United States stands with Kenya's leadership "against this terrible outrage that's occurred."