The White House condemned as "despicable" the attack that left at least 39 people dead at a Nairobi shopping mall Saturday, vowing to assist Kenya's counterterrorism efforts.

Americans were among the injured -- estimated at 150 -- in the attack claimed by Somalia's Al-Qaeda-linked Shebab militants, US Secretary of State John Kerry said.

Although no Americans are known to have died in the attack, he confirmed that one of those killed was the wife of a foreign national working for the US Agency for International Development.

"Today's terrorist massacre of so many innocents is a heartbreaking reminder that there exists unspeakable evil in our world which can destroy life in a senseless instant," Kerry added.

"Attacks like this can't change who we are, a people committed to peace and justice for all, but rather must reaffirm our determination to counter extremism and promote tolerance everywhere."

The top US diplomat promised to help bring the perpetrators of the "abhorrent violence" to justice.

"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."

Offering Washington's "deepest condolences" to victims' families and loved ones, Hayden vowed to "stand with the Kenyan people in their efforts to confront terrorism in all its forms, including the threat posed by al-Shebab."

"This cowardly act against innocent civilians will not shake our resolve," she added.

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."

Gunmen were still holding hostages at the mall more than 12 hours after the attack began, while security forces tried to secure the area and neutralize the attackers, officials said.

"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."

Paris said two French citizens were among those killed in the attack and Britain has warned that some of its citizens may have been injured or killed.