"There are countless number of dead bodies still scattered inside the mall, and the mujahideen are still holding their ground," the Somali rebel group al-Shabab said in one Twitter message considered to be genuine.
It added it still held hostages, who were "still alive looking quite disconcerted but, nevertheless, alive."
Kenyatta did not mention the fate of the hostages — if it was indeed true that there were still some being held — in his address.
Al-Shabab, whose name means "The Youth" in Arabic, said the mall attack was in retribution for Kenyan forces' 2011 push into neighboring Somalia. African Union forces pushed the al-Qaida-affiliated group out of Somalia's capital in 2011.
"You could have avoided all this and lived your lives with relative safety," the group Tweeted Tuesday. "Remove your forces from our country and peace will come."
Kenyatta said "initial reports had suggested that a British woman and two or three American citizens may have been involved in the attack," but that "we cannot confirm the details at the moment.
He said experts were working to try and determine the nationalities of the terrorists.
Earlier, Kenyan Foreign Minister Amina Mohamed had said "two or three Americans" and "one Brit" were among those who attacked the mall.
A security expert with contacts inside the mall described the attackers as "a multinational collection from all over the world."
U.S. officials said they were looking into whether any Americans were involved. State Department spokeswoman Jen Psaki said Monday that the department had "no definitive evidence of the nationalities or the identities" of the attackers.
Britain's foreign office said it was aware of the Kenyan foreign minister's remarks, but would not confirm if a British woman was involved.
Al-Shabab, responding to a request from AP, denied that any women had attacked the mall, saying "these are just baseless rumors."
"We have an adequate number of young men who fully committed and ready to sacrifice their lives for the sake of Allah and for the sake of their religion," said the al-Shabab press office in what is thought to be an authentic email address.
The attack began on Saturday when an estimated 12 to 15 al-Shabab militants invaded the mall, wielding grenades and firing on civilians inside the complex, which includes shops for Nike, Adidas and Bose and is popular with foreigners and wealthy Kenyans.
The militants specifically targeted non-Muslims, and at least 18 foreigners were among the dead, including six Britons, as well as citizens from France, Canada, the Netherlands, Australia, Peru, India, Ghana, South Africa and China. Nearly 200 people were wounded, including five Americans.
A U.S. Embassy vehicle, identifiable by its numbered diplomatic license plate, arrived at the morgue on Tuesday. American officials have not confirmed the deaths of any U.S. citizens in the mall attack, but it appeared possible the Americans who visited the morgue — likely security officials with an agency like the FBI — could have been seeking information about one of the bodies inside.
The attack at the Westgate mall in Nairobi's Westlands neighborhood was the deadliest terrorist attack in Kenya since the 1998 al-Qaida truck bombing of the U.S. Embassy in Nairobi, which killed more than 200 people.