WASHINGTON (AFP) - 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 reportedly among the injured - estimated at 150 - in the attack claimed by Somalia's Al-Qaeda-linked Shebab militants, the US State Department said.

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

"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." 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," Mr 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.

State Department spokesman Marie Harf had earlier decried the "senseless act of violence."