The attack by al-Qaida-linked militants at an upscale mall in Nairobi killed at least 59 people and wounded 175, Kenya's interior Cabinet secretary said Sunday.

Multiple barrages of gunfire erupted Sunday morning from inside the building where there is a hostage standoff with Islamic extremists nearly 24 hours after they attacked using grenades and assault rifles.

"The priority is to save as many lives as possible," Joseph Lenku said, reassuring the families of the hostages in the upscale Westgate mall. Kenyan forces have already rescued about 1,000 people, he said.

Lenku said that there are 10 to 15 attackers involved, and Kenyan forces have control of the security cameras inside the mall. Combined military and police forces surrounded the building.

Former Kenyan Prime Minister Raila Odinga told reporters at the mall that he has been told officials couldn't determine the exact number of hostages inside the mall.

"There are quite a number of people still being held hostage on the third floor and the basement area where the terrorists are still in charge," Odinga said.

Somalia's al-Qaida-linked rebel group, al-Shabab, claimed responsibility for the attack in which they specifically targeted non-Muslims.

Kenyans and foreigners were among those confirmed dead, including French, Canadians and Chinese.

The Chinese Embassy in Kenya said in a statement Sunday that a 38-year-old Chinese woman had been killed in the shopping mall "terror attack." Her son was injured in the attack and in a stable condition in hospital, according to the statement posted on the embassy's website.

Kenya's presidential office said that one of the attackers was arrested on Saturday and died after suffering from bullet wounds.

Trucks brought in a fresh contingent of soldiers from the Kenya Defense Forces early Sunday.

"Violent extremists continue to occupy Westgate Mall. Security services are there in full force," said the United States embassy in an emergency text message issued Sunday morning.

Daylight brought some good news, as Kenyan media reported that several people in hiding in the mall escaped to safety, suggesting that not everyone who is still inside is being held by al-Shabab.

Cecile Ndwiga said she had been hiding under a car in the basement parking garage.

"I called my husband to ask the soldiers to come and rescue me. Because I couldn't just walk out anyhow. The shootout was all over here _ left, right_ just gun shots," she said.

Nairobi resident Paolo Abenavoli said he is holed up in his apartment only 100 meters from the mall with a direct view of the entrance. He said he could see a dozen or more security forces inside a first floor restaurant.

"The battle is on now," Abenavoli told The Associated Press by telephone as the fresh gunfire broke out Sunday.

Security forces had pushed curious crowds far back from the mall. Hundreds of residents gathered on a high ridge above the mall to watch for any activity.

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Associated Press reporter Louise Watt in Beijing contributed to this report.