Americans were reportedly among the injured -- estimated at 150 -- in the attack claimed by Somalia's Al-Qaeda-linked Shebab militants, the US State Department said yesterday.
"The United States condemns in the strongest terms the despicable terrorist attack on innocent civilians today at the Westgate Shopping Mall in Nairobi, Kenya," US National Security Council spokeswoman Caitlin Hayden said in a statement.
"The perpetrators of this heinous act must be brought to justice, and we have offered our full support to the Kenyan Government to do so."
"This cowardly act against innocent civilians will not shake our resolve," she added.
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Saying he had lost family members in the violence, Kenyan President Uhuru Kenyatta said his country had "overcome terrorist attacks before, and we will defeat them again."
Security forces were still in the process of trying to secure the mall and neutralise the attackers, according to the president.
"They want to cause fear and despondency in our country, but we will not be cowed," Kenyatta said about the fighters. "Terrorism is a philosophy of cowards."
State Department spokeswoman Marie Harf had earlier decried the "senseless act of violence.