NAIROBI, Kenya — Terrified shoppers huddled in back hallways and prayed they would not be found by the Islamic extremist gunmen lobbing grenades and firing assault rifles inside Nairobi’s top mall Saturday. When the coast was thought to be clear, crying mothers clutching small children and blood-splattered men sprinted out of the four-story mall.

At least 30 people were killed in the assault, with fears the toll could rise further, said Kenya Red Cross official Abbas Gullet.

The al-Qaida-linked gunmen asked the victims they had cornered if they were Muslim: If the answer was yes, several witnesses said, those people were free to go. The non-Muslims were not.

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

Foreigners are expected to be among the casualties. There are reports of American citizens injured in the attack but the United States State Department said it had no further details.

As night fell in Kenya’s capital, hostages remained inside the mall, but officials didn’t or couldn’t say how many. Two contingents of army special forces troops had moved inside as the stand-off stretched into its ninth hour.

Police and military surrounded the huge shopping complex as helicopters buzzed overhead. An Associated Press reporter said he saw a wounded Kenyan soldier put into an ambulance at nightfall, an indication, perhaps, of a continuing shoot-out inside.

Witnesses said at least five gunmen — including at least one woman — first attacked an outdoor cafe at Nairobi’s Westgate Mall, a shiny, new shopping center that hosts 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 — expatriates and rich Kenyans — fled in any direction that might be safe: 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, 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. The others were black,” he said.

Al-Shabab, on its Twitter feed, said that it has many times 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 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.

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 U.S. embassy said it was in contact with local authorities and offered assistance. Some British security personnel assisted in the response.

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.