NAIROBI, Kenya (CNN) -- Fifty-nine dead. At least 175 injured. About 30 hostages still inside, as well as perhaps a dozen gunmen.Those are the grim numbers, a day after attackers stormed an upscale Nairobi mall, spraying bullets and holding shoppers captive.
Kenya's President Uhuru Kenyatta told reporters Sunday afternoon the tragedy was personal; one of his nephews and his fiancee were among the 59 people killed.
"We will punish the masterminds (of the attack) swiftly, and indeed very painfully," Kenyatta said.
Kenyan government and Western diplomatic sources said Al-Shabaab militants were holding about 30 hostages inside the shopping center.
By noon Sunday, as grim-faced Kenyan soldiers warily searched the five-story building -- and as Al-Shabaab maintained its defiant stance -- the siege was no closer to a resolution.
Officials believe 10 to 15 gunmen are involved, State House spokesman Manoah Esipisu said Sunday.
"We know that they were across the building," Esipisu told CNN's Zain Verjee. "We know that they are now isolated somewhere within the building."
More than 175 were injured in the attack, Kenyatta said.
It was the deadliest terror attack in the nation since al Qaeda blew up the U.S. Embassy in 1998, killing more than 200 people.
The attack Saturday targeted a popular weekend meeting spot. Kenyans and expatriates gather at the luxurious Westgate mall on weekends to drink lattes, catch a movie or browse through the more than 80 stores.
Al-Shabaab, al Qaeda's proxy in Somalia, claimed responsibility, and said it was not backing down. In a message on its Twitter feed, the group said "all Muslims" were escorted from the mall before the attack.
"When justice is denied, it must be enforced," it said in a tweet Sunday. "Kenyans were relatively safe in their cities before they invaded us & killed Muslims #Westgate"
As the sun rose Sunday, the standoff between Kenyan forces and the attackers continued.
Soldiers kept vigil outside the mall, guns dangling from their shoulders.
"We want to do everything possible, and the security people are doing everything possible to make sure we lose no more lives," Esipisu said.
Three injured security forces were taken out of the besieged mall, but the severity of their injuries was unclear.
By midday Sunday, at least 1,000 people had been freed from the mall, Esipisu said. "Our priority is now those that remain inside."
An apparent hostage left the building Sunday, and said she had been hiding in the basement of the mall, CNN affiliate KTN reported.
Al-Shabaab vowed not to negotiate with Kenyan authorities.
"The Mujahideen are still strong inside #Westgate Mall and still holding their ground," the group tweeted late Saturday.
Israeli special forces are at the scene and are working with their Kenyan counterparts in the hostage crisis, Kenyan government sources tell CNN.
Esipisu said there were reports of a white woman among the hostage takers. Kenyan intelligence officials were investigating the claims, he said.
Esipisu was asked if the reported woman was thought to be the infamous Al-Shabaab-affiliated "White Widow," Samantha Lewthwaite. "Nothing is being ruled out," he said.
But CNN terrrorism analyst Peter Bergen said it was unlikely.
"It would be very unusual for a woman to be involved in one of these operations," he said. "Typically these groups are misogynist. Their view is the woman should be in a home and shrouded in a body veil."
Lewthwaite's husband, Germaine Lindsey, was one of the suicide bombers killed in the 2005 attack on London's transportation system. His Buckinghamshire-born widow is wanted by Kenyan authorities for her alleged role as an Al-Shabaab and al Qaeda-linked financier.
A day of horror
The calm was shattered around noon local time Saturday. Gunshots erupted as shoppers picked up groceries, savored lunch and browsed through the racks at stores.
Before long, pools of blood smeared pristine hallways. Bodies lay strewn across the floor.
Uche Kaigwa-Okoye was sipping coffee when he heard what first sounded like a fallen table, then the continuing rat-a-tat of gunfire. As the gunshots became louder, screaming crowds headed for the exits.
He joined 20 people who took shelter for about five hours in a women's bathroom cubicle.
"They had grenades, and it was really, really loud," he said of the attackers. He noticed tear gas in the hallways as well.
"All of us felt like they were close," he said.
As people texted family and friends outside the mall, word spread that nobody could be trusted. And even if the good guys could be sorted from the bad guys, the intermittent barrages of gunfire made any escape attempt seem futile.
Sara Head, a Washington resident, experienced similar horror in the mall's parking garage. As her car pulled up, she heard gunfire. She crawled underneath and hid behind cars before getting into a stairwell.
Eventually, the stairwell lights came back on and the door to a nearby supermarket opened. She dashed through, passed a nearby loading dock and fled to safety.
"There was blood throughout the supermarket," Head said. "It wasn't clear if it was OK to exit."
The national disaster agency reported early Sunday morning that five "visibly shaken" hostages had been released. It said "major operations underway." What that meant was a mystery.
Foreigners among casualties
Most of the casualties are Kenyan, authorities said. But the mall is popular with expatriates and foreign nationals, who were among those killed and injured.
Those killed include three British citizens, two French nationals and two Canadians, including a diplomat, their governments said.
Several American citizens were among the wounded, including Elaine Dang, a University of California, Berkeley, graduate.
Dang worked as the general manager for Eat Out Kenya, which confirmed her injuries on its Twitter and Facebook pages.
The State Department said Saturday there were several Americans among the injured, but none among the dead. Secretary of State John Kerry didn't offer details.
The U.S. Embassy is asking personnel to stay in place Sunday and avoid the Westgate Mall area and any large gatherings. All U.S. citizens in Kenya are urged to register online so the embassy can provide them with updated information on travel and security -- and can contact them in case of emergency.
Israel's Foreign Ministry said one national was slightly wounded and three escaped. A cafe at the mall is owned by an Israeli, but the ministry does not believe the mall was targeted because of that.
The Ghana president's office said literary figure Kofi Awoonor was among those killed in the attack.
"Such a sad twist of fate to place Prof at the wrong place at the wrong time," President John Mahama said in a statement.
A plea for blood
Several Kenyan agencies made a plea for blood donations.
"Hospitals are appealing for more blood, the response is incredible but more is needed," tweeted Francis Kimemia, secretary to the Cabinet.
And as the nation grappled with the aftermath, Kenyatta blasted "the despicable perpetrators of this cowardly act," and said they will be brought to justice.
'We shall hunt down the perpetrators'
Kenya is no stranger to terrorism.
A 1998 bombing at the U.S. Embassy in Nairobi left 213 dead. Al Qaeda claimed responsibility for the attack.
Since Kenya launched attacks against Al-Shabaab in Somalia in 2011, the group has hurled grenades at Kenyan churches, bus stops and other public places.
In a televised speech late Saturday, Kenyatta said his nation has "overcome" attacks before, refusing to budge from its values or relinquish its security. And it will do so again, he promised.
"We shall hunt down the perpetrators wherever they run to," the president said. "We shall get them, and we shall punish them for this heinous crime."
But first, authorities will have to get to all the assailants and hostages still inside the mall.
CNN's Faith Karimi, Holly Yan and Greg Botelho reported and wrote from Atlanta; Lillian Lesposo reported from Nairobi. CNN's Tim Lister, Nima Elbagir, Joseph Netto, Boriana Milanova, Jamie Crawford, Stefan Simons, Karen Smith and Azadeh Ansari contributed to this report.