At least 39 people were killed and more than 150 wounded by Islamic extremist gunmen in an assault inside Nairobi’s top mall early today. Kenya’s president announced the attack on national TV, while disclosing that his close family members were among the dead. AP reports that terrified shoppers huddled in back hallways and prayed they would not be found by the terrorists lobbing grenades and firing assault rifles inside the mall.

When the coast was thought clear, crying mothers clutching small children and blood-splattered men sprinted out of the mall. As of early Sunday morning, about 12 hours after the attack began, gunmen remained holed up inside the mall with an unknown number of hostages. President Uhuru Kenyatta called the security operation under way “delicate”. Kenyatta said the top priority was to safeguard hostages.

As the attack unfolded shortly after noon Saturday, the al-Qaida-linked gunmen asked the victims they had cornered if they were Muslim. If the hostages answered yes, several witnesses said, those people were free to go. The non-Muslims were held. Police and military surrounded the huge shopping complex as helicopters buzzed overhead. An Associated Press reporter witnessed a wounded Kenyan soldier put into an ambulance at nightfall. Perhaps an indication of a continuing shoot-out inside.

The attack began shortly after noon with bursts of gunfire and grenades. Shoppers, mostly expatriates and rich Kenyans, fled to anywhere that might be safe, like into back corners of stores, back service hallways and bank vaults. Over the next several hours, pockets of terrified people poured out of the mall as undercover police moved in and some of the wounded mall goers 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, the restaurant with shady outdoor seating.

Frank Mugungu, an off-duty army sergeant major, said he saw four male attackers and one female attacker. “One was Somali,” he said, but the others were black, suggesting that they could have been Kenyan or another nationality.

Somalia’s Islamic extremist group al-Shabab claimed responsibility and said the attack was retribution for Kenyan forces’ 2011 push into Somalia. The rebels then 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. They also said that it has many times warned Kenya’s government that failure to remove its forces from Somalia “would have severe consequences.” Al-Shabab claimed that its gunmen had killed 100 people, but its assertions are often exaggerated.

Al-Shabab reportedly threatened in late 2011 to unleash a large-scale attack in Nairobi. Kenya has seen a regular spate of grenade attacks since then. However, they have never such a large terrorist assault. Anti-terror Police Unit boss Boniface Mwaniki said vests found were similar to those used in attacks that killed 76 people in Uganda. Those people had gathered to watch the soccer World Cup finals on TV in July 2010. Al-Shabab claimed responsibility for those bombings, saying the attack was in retaliation for Uganda’s participation in the African Union’s peacekeeping mission in Somalia.

“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.”

The U.S. embassy said it was in contact with local authorities and offered assistance and some British security personnel assisted in the response.The U.S. State Department condemned “this senseless act of violence that has resulted in death and injury for many innocent men, women, and children.”

The local hospital was overwhelmed with the number of wounded being brought in hours after the attack, so much so, that they had to divert them to a second facility. Dozens of people were seriously wounded. Officials said Kenyans turned out in droves to donate blood.

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.

The 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 sought cover on an upper floor in the mall when shooting began. He said that when he looked out of a window onto the upper parking deck of the mall he saw the shooters 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.

The gunmen carried AK-47s and they wore vests with hand grenades on them, said Manish Turohit. He stayed alive by hiding in a parking garage for two hours. “They just came in and threw a grenade. We were running and they opened fire. They were shouting and firing,” he said after marching out of the mall in a line of 15 people who all held their hands in the air.

“These heartless acts against defenseless civilians, including innocent children, are beyond the pale and cannot be tolerated. We stand shoulder to shoulder with Kenya in its time of grief for these lives lost and the many injured,” President Hassan Sheikh Mohamud said. Somalia’s president, obviously familiar with terrorist attacks, said his country knows “only too well the human costs of violence like this” as he extended his prayers to those in Kenya.

The United Nations Secretary General’s office said that Ban Ki-moon has spoken with President Uhuru Kenyatta and expressed his concern and British Prime Minister David Cameron also called Kenyatta and offered his assistance.

The attack was carried out by terrorists, said Kenyan police chief Benson Kibue. He did not specify a group. He said it was likely that no more than 10 attackers were involved.