NAIROBI, Kenya—The terrorist siege of an upscale Kenyan shopping center by a group of gunmen, already responsible for 59 deaths, continued into a second day Sunday as soldiers and police tried to corner the attackers inside the mall while evacuating the wounded.
Kenyan officials said that they were making progress in securing the building as the death toll rose. Occasional gunshots could be heard throughout the morning.
Saturday's attack started shortly after midday when about a dozen gunmen burst into Westgate mall in the capital, opening fire and throwing grenades in a terrorist attack claimed by Somalia's al-Shabaab militant group.
At least 59 people have been confirmed killed so far and more than 175 wounded, said Joseph Ole Lenku, the cabinet secretary for the interior. He said more than 1,000 people had been safely evacuated from the mall.
Mr. Ole Lenku urged Kenyans to be patient while security forces pursue the attackers carefully in order to prevent more civilian deaths.
"Our priority remains that we save as much life as possible, and that is what makes this operation very, very delicate," he said. He said that they believed there were between 10 and 15 attackers. He declined to estimate how many civilians were still in the mall or to confirm if any of them were being held hostage.
Mr. Ole Lenku said the Kenyan government hasn't had any direct communication with the attackers, but the government has gained control of the closed-circuit television used to monitor the mall.
Several foreigners were among the dead, as well as family members of Kenya's president.
In a television address late Saturday, Kenyan President Uhuru Kenyatta offered his condolences to those who lost loved ones—and included himself in that group.
"I know what you feel having also personally lost very close family members in this attack," Mr. Kenyatta said, without elaborating further.
The death toll is expected to rise as police make their way through the large complex, which has three main floors and a smaller fourth floor housing a movie theater, to confront the assailants.
Saturday's rampage was the deadliest single attack in Nairobi since the 1998 bombing of the U.S. Embassy that killed more than 200 people, and is thought to have been carried out by Somali militants.
Canada said two of its citizens, including a diplomat, were among the dead, and the U.S. said that the wife of a foreign service national working for the U.S. Agency for International Development was killed and that American citizens were reported among the injured.
Patrons of the mall were sitting down for lunch or strolling through the facility when cars packed with an unknown number of gunmen drove up to the main entrance of the mall around 12:30 p.m. and started shooting as they rushed through the open doors where guests usually wait in line to have their bags checked by security guards, witnesses said.
The attackers shot into the crowds of people at outdoor restaurants and pushed farther into the mall, firing their weapons and throwing grenades as they raced to the higher levels of the mall. Shoppers crawled into back storerooms and bathrooms, locking doors where they could. At least one bank was able to lock its customers in a safe room, witnesses said. Those near exits raced out of the mall, some taking refuge in nearby apartment buildings to catch their breath and call family members.
Police arrived and cordoned off the parking lot, at first believing they were dealing with a robbery attempt. But as wounded survivors started piling into ambulances it became clear that the attackers had opened fire, that they hadn't appeared to be after anything and that they seemed to be targeting non-Muslims.
Police and military forces slowly started the work of pushing into the mall and pulling out those hiding and the injured while trying to close in on the attackers without knowing exactly how many assailants there were or where they were shooting from.
As survivors emerged, some with their hands up to show they weren't carrying weapons, Red Cross workers escorted them to a nearby building and assured them they were safe.
Somalia's al-Shabaab militant group, which has said it was planning an attack in Nairobi as retribution for Kenya sending troops into Somalia to fight the group, appeared to claim responsibility for the attack.
A posting on a Twitter account that has been used by al-Shabaab said the attackers belonged to their group. The Kenyan government "is pleading with our Mujahideen inside the mall for negotiations. There will be no negotiations," the author wrote.
Witnesses gave conflicting accounts about the attackers' appearance, with some saying they looked foreign and spoke Somali—a few wore long beards, which are uncommon in Kenya—and some wore turbans.
"I saw two men with white turbans and guns," said George Onyango, who ran out of the mall with two members of the family he works for and hid on the floor of his car as the attackers ran in. He said the attackers were shouting in Somali and running up to the top floor.
Another witness, 59-year old French national Marcel Hale, said he saw a bearded gunman shooting toward him and yelling, "Allahu akbar!" Arabic for "God is Great!" Mr. Hale said that the bullet hit a stool and that he and his wife ran to a restaurant kitchen, where they hid until they were rescued by police. Both of them escaped unharmed.
Other witnesses said the attackers didn't look foreign at all.
"They could have been Kenyans," said Sheila Akaliche, a waitress at a restaurant in the mall who saw the attackers enter and start shooting at diners. She said she saw two men wearing western clothes—black shirts and pants. Then she ran. Her colleague was shot in the arm as they fled.
Nor was it clear how many assailants there were, but a policeman at the site, who declined to be identified because he wasn't authorized to speak to the media, said there was more than one car full of men. The Kenyan police inspector general, David Kimaiyo, said in a tweet that one gunman was wounded and that several others were pinned down by gunfire but didn't say how many attackers were there.
As night fell, many of those still trapped inside who had been sending text messages to friends started turning off their phones to conserve their batteries.
Canadian Prime Minister Stephen Harper said Annemarie Desloges, a liaison officer at Canada's High Commission to Kenya, was killed in the attack. Mr. Harper said Canada condemns "in the strongest possible terms this cowardly, hateful act."
The U.S. State Department said it had reports that U.S. citizens were injured in the attack. "We condemn this senseless act of violence," a spokeswoman said.
Westgate Mall is a regular weekend lunch and shopping destination for the country's new consumer class as well as foreign officials working at nearby embassies in Nairobi. On Saturday, the mall had been hosting a children's cooking event. It wasn't known what happened to the participants in the event.
Guards at the main entrance use metal detectors to check for weapons and search handbags before shoppers enter, a common precaution in high-crime Nairobi. The entrance itself isn't reinforced or protected from the street.
Although small-scale grenade attacks have taken place recently in Kenya's capital, large-scale and organized assaults are rare. Naeem Biviji, a 34-year-old who owns a furniture company with his wife, said they had been having lunch at one of the mall's outdoor cafes with two friends visiting from England when they heard shooting and dove to the floor. They crawled to a stairwell and eventually ran out a side entrance, his wife Bethan carrying their 7-month-old baby in her arms.
"We heard a lot of shooting and then one or two big booms," said Mr. Biviji. "The whole place smelled like fireworks." Neither he nor his companions saw the attackers.
Those who managed to get out of the mall said they were sending and receiving text messages inside about where the attackers were or what they might want.
Israeli businessman Eran Ochayon said that he received a text message saying that the assailants were asking people to recite the names of God in Arabic. to show that they were Muslim and should therefore be spared. Mr. Ochayon wrote a number of the names on his hand in case he needed them. He said he also tossed aside his passport so he could not be identified as Israeli.
"I was assuming they were going to come in any second," he said. He waited like that, inside the locked Barclay's Bank branch, for hours before police came banging on the door and escorted him to safety.
—Idil Abshir in Nairobi and Karen Johnson in Ottawa contributed to this article.
