At least 39 people were killed and more than 150 wounded by Islamic extremist gunmen who shot non-Muslims with assault rifles and let Muslims go in a midday attack at a Nairobi mall, according to a report by CBSNews.

Twelve hours after the attack began, gunmen remained in the mall with hostages, the report said.

Somalia’s Islamic extremist group al-Shabab claimed responsibility and said the attack was payback for Kenyan forces’ push into Somalia in 2011. They threatened more attacks.

Al-Shabab said on its Twitter feed that Kenyan security officials were trying to open negotiations. “There will be no negotiations whatsoever,” al-Shabab tweeted.

As night fell in Kenya’s capital, two contingents of army special forces troops moved inside the mall.

Witnesses said at least five gunmen including at least one woman first attacked an outdoor cafe at Nairobi’s Westgate Mall, a new shopping center with Nike, Adidas and Bose stores. The mall’s ownership is Israeli, and security experts have long said the structure made an attractive terrorist target.

The attack began shortly after noon with bursts of gunfire and grenades. Shoppers fled into back corners of stores, back service hallways and bank vaults. Over the next several hours, pockets of people poured out of the mall as undercover police moved in. Some of the wounded were moved out in shopping carts.

“We started by hearing gunshots downstairs and outside. Later we heard them come inside. We took cover. Then we saw two gunmen wearing black turbans. I saw them shoot,” said Patrick Kuria, an employee at Artcaffe.

Kenya’s president said on national TV that his close family members were among the dead.

Foreigners were among the casualties. France’s president said that two French women were killed, and there were reports of American citizens injured, but the U.S. State Department said it had no further details.

A spokesman for the U.S. Embassy in Nairobi told CBS News that all American embassy personnel were safe and all but a handful of Kenyans who work for the embassy were accounted for.

The White House condemned the attack as a “despicable terrorist attack on innocent civilians.”

“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,” National Security Council spokeswoman Caitlin Hayden said in a statement.

On its Twitter feed, Al-Shabab said that it has often warned Kenya’s government that failure to remove its forces from Somalia “would have severe consequences.” The group claimed that its gunmen had killed 100 people, but its assertions are often exaggerated, the report said.

“The attack at #WestgateMall is just a very tiny fraction of what Muslims in Somalia experience at the hands of Kenyan invaders,” al-Shabab said. Another tweet said: “For long we have waged war against the Kenyans in our land, now it’s time to shift the battleground and take the war to their land #Westgate.”

Al-Shabab threatened in late 2011 to unleash a large-scale attack in Nairobi. Kenya has seen a regular spate of grenade attacks since then but never such a large terrorist assault.

Nairobi’s mortuary superintendent, Sammy Nyongesa Jacob, said Africans, Asians and Caucasians were among the bodies brought to the mortuary.

Gunmen told hostages that non-Muslims would be targeted, said Elijah Kamau, who was at the mall at the time of the midday attack.

“The gunmen told Muslims to stand up and leave. They were safe, and non-Muslims would be targeted,” he said.

Jay Patel, who sought cover on an upper floor in the mall when shooting began, said that when he looked out of a window onto the upper parking deck of the mall he saw the gunmen with a group of people. Patel said that as the attackers were talking, some of the people stood up and left and the others were shot.

Somalia’s president said his country knows “only too well the human costs of violence like this” as he extended prayers to those in Kenya.

A local hospital was overwhelmed with the wounded and had to divert them to a second facility. Dozens of people were wounded. Officials said Kenyans turned out in droves to donate blood.