"We will punish the masterminds (of the attack) swiftly, and indeed very painfully," Kenyatta said.
Kenyan government and Western diplomatic sources said Al-Shabaab militants were holding about 30 hostages inside the shopping center.
By noon Sunday, as grim-faced Kenyan soldiers warily searched the five-story building -- and as Al-Shabaab maintained its defiant stance -- the siege was no closer to a resolution.
Officials believe 10 to 15 gunmen are involved, State House spokesman Manoah Esipisu said Sunday.
"We know that they were across the building," Esipisu told CNN's Zain Verjee. "We know that they are now isolated somewhere within the building."
More than 175 were injured in the attack, Kenyatta said.
It was the deadliest terror attack in the nation since al Qaeda blew up the U.S. Embassy in 1998, killing more than 200 people.
Africa's growing modernity, especially in large cities like Nairobi, make tempting targets for AQ and its affiliates. Still, going into a mall, executing non-Muslims, and taking dozens of hostages is brazen even for those willing to die to further their aims. Here's hoping that no more hostages or Kenyan military are killed.