Story highlights The number of hostages believed to be held drops to 10 or less

Security forces are reported to have taken control of most of the mall

Three of the alleged attackers are believed to be from the United States

At least 68 people have been killed, another 175 injured

Authorities in Kenya appeared close to ending a deadly siege Monday at an upscale Nairobi mall, where attackers have killed at least 68 people, injured 175, and are believed to still be holding about 10 people hostage.

"All efforts are underway to bring this matter to a speedy conclusion," the Kenyan military announced on Twitter.

It said that "most of the hostages have been rescued and security forces have taken control of most parts of the building."

Earlier, police had tweeted that a "MAJOR assault" by security forces was ongoing.

The developments come some two days after Al-Shabaab militants first stormed the shopping center, spraying bullets and unleashing chaos.

Photos: Photos: Kenya mall attack Photos: Photos: Kenya mall attack Kenya mall attack – Relatives of Johnny Mutinda Musango, 48, weep after identifying his body at the city morgue in Nairobi, Kenya, on Tuesday, September 24. Musango was one of the victims of the Westgate Mall hostage siege. Kenyan security forces were still combing the mall on the fourth day of the siege by al Qaeda-linked terrorists. Hide Caption 1 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Ann Gakii reacts at the Nairobi City Mortuary after identifying the body of her father, who was killed in the mall attack on Saturday. Hide Caption 2 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A Kenyan soldier runs through a corridor on an upper floor at the Westgate Shopping Mall in Nairobi, Kenya, on September 24, shortly before an explosion was heard. Sounds of heavy gunfire erupted from the mall Tuesday, even as authorities said they had the building under their control. But four days after Al-Shabaab terrorists stormed the swanky mall, several gunmen -- including snipers -- were still inside, two senior officials said. Hide Caption 3 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Kenyan Defense Forces walk near the mall on Monday, September 23. Hide Caption 4 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Kenyan Defense Forces leave the mall on September 23. Hide Caption 5 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Stephen, center, is comforted by relatives as he waits for the post mortem exam of his father, who was killed in Saturday's attack at the mall. Hide Caption 6 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A Kenyan police officer guards the entrance of a building near the mall on September 23. Hide Caption 7 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A Kenyan security officer takes cover as gunfire and explosions are heard from the mall on September 23. Hide Caption 8 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Heavy smoke rises from the Westgate Shopping Mall on September 23. Hide Caption 9 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Medics take cover behind a tree as gunfire and explosions are heard from the Westgate Mall on September 23. Hide Caption 10 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A Kenyan police security officer runs for cover as heavy smoke rises from the mall on September 23. Hide Caption 11 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A paramedic runs for cover outside the mall on September 23. Hide Caption 12 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – People run for cover outside the mall after heavy shooting started on September 23. Hide Caption 13 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Kenyan security forces crouch behind a wall outside the mall on September 23. Hide Caption 14 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Soldiers take cover after gunfire near the mall on September 23. Hide Caption 15 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Kenyan paramilitary police officers patrol the area near the mall on Sunday, September 22. Hide Caption 16 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Soldiers from the Kenya Defense Forces arrive outside the Westgate Mall on September 22. Hide Caption 17 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A woman shields a baby as a soldier stands guard inside the Westgate Mall on Saturday, September 21. Hide Caption 18 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A rescue worker helps a child outside the mall. Hide Caption 19 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – People who had been hiding inside the mall during the gunfire flee the scene. Hide Caption 20 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – An armed official takes a shooting position inside the mall. Hide Caption 21 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – An armed official crouches on September 21. Hide Caption 22 of 51 Photos: Photos: Kenya mall attack Hide Caption 23 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Bodies lie on the ground inside the mall. Hide Caption 24 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Men help a wounded woman outside the mall. Hide Caption 25 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Officials carry an injured man in the mall. Hide Caption 26 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Soldiers move up stairs inside the Westgate Mall. Hide Caption 27 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Armed police leave after entering the mall. At least one suspect has been killed, a government official said. Police have said another suspected gunman has been detained at a Nairobi hospital. Hide Caption 28 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Armed police take cover behind escalators as smoke fills the air. Witnesses say tear gas was thrown in the corridors. Hide Caption 29 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A woman who had been hiding during the attack runs for cover after armed police enter the mall. Hide Caption 30 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A body is seen on the floor inside the smoke-filled four-story mall. Hide Caption 31 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – An injured person is helped on arrival at the Aga Khan Hospital in Nairobi after the attack at the upscale mall. Hide Caption 32 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A soldier directs people up a stairway inside the Westgate on September 21. Hide Caption 33 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – An injured man is wheeled into the Aga Khan Hospital in Nairobi. Hide Caption 34 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – People run from the Westgate Mall. Hide Caption 35 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A Kenyan woman is helped to safety after the masked gunmen stormed the upscale mall and sprayed gunfire on shoppers and staff. Hide Caption 36 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Crowds gather outside the upscale shopping mall. The interior ministry urges Kenyans to keep off the roads near the mall so police can ensure everyone inside has been evacuated to safety. Hide Caption 37 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A policeman carries a baby to safety. Authorities said multiple shooters were at the scene. Hide Caption 38 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Bodies lie outside the shopping mall. Hide Caption 39 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A security officer helps a wounded woman outside. Hide Caption 40 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Elaine Dang of San Diego is helped to safety after the attack. The military asked local media not to televise anything live because the gunmen are watching the screens in the mall. Hide Caption 41 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Paramedics treat an injured man outside the mall. Hide Caption 42 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Medical personnel carry a body away. Hide Caption 43 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A body lies outside the mall. Gunmen shot people outside the mall as they entered it Hide Caption 44 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A woman is pulled by a shopping cart to an ambulance. Hide Caption 45 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A wounded man is escorted outside the mall. Hide Caption 46 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A police officer carries a baby as people keep low and run to safety. Crowds dashed down the streets as soldiers in military fatigues, guns cocked, crawled under cars to get closer to the mall. Hide Caption 47 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – People run away from the scene. Hide Caption 48 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – Armed Kenyan forces take position to secure the area around the shopping mall as ambulances move in to carry the injured. Hide Caption 49 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A woman reacts after she is rescued from the mall. Hide Caption 50 of 51 Photos: Photos: Kenya mall attack Kenya mall attack – A couple flee the area. As night fell, authorities said they had cornered the gunmen in the mall. Hide Caption 51 of 51

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There are believed to be between 10-15 gunmen involved in the attack, officials said.

Sources within Al-Shabaab told CNN that nine names listed on a Twitter site -- now suspended -- were people who were among the alleged hostage-takers.

Three of the alleged attackers are from the United States, two are from Somalia and there is one each from Canada, Finland, Kenya and the United Kingdom, according to the list.

The FBI is looking into the claim that American citizens were involved the attack, but have not confirmed that.

Similarly, a senior State Department official said that the United States is trying to determine whether any of the alleged attackers are American. But, the official said, authorities are becoming more confident American citizens were involved.

Kenyan President Uhuru Kenyatta vowed Sunday to hold those responsible for the violence, accountable.

The tragedy is personal for the president; one of his nephews and his fiancee were among the dead.

"They shall not get away with their despicable, beastly acts. Like the cowardly perpetrators now cornered in the building, we will punish the masterminds swiftly and indeed very painfully," Kenyatta said.

'Bunch of cowards'

Sporadic gunfire could be heard throughout the day Sunday, and at least one explosion. Those sounds were followed by periods of tense silence.

Soldiers kept vigil outside the mall, guns dangling from their shoulders. Later in the day, helicopters approached.

The Kenyan Red Cross tweeted that nine bodies were recovered Sunday night, bringing the death toll to 68.

More than 175 were injured in the attack, Kenyatta said. He and other Kenyan officials visited hospitals Sunday morning.

"No one should lose their life so needlessly, so senselessly and no family should have to receive news that their loved ones have been killed by a criminal bunch of cowards," the president said.

The mall siege was the deadliest terror attack in Kenya since al Qaeda blew up the U.S. Embassy there in 1998, killing 213 people.

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"

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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.

Last year, the Kenyan military played a major role in handing Al-Shabaab forces a defeat when as part of a peacekeeping mission, they liberated the key Somali port of Kismayo.

The attack Saturday targeted a popular weekend meeting spot. Kenyans and expatriates gather at the luxurious Westgate Shopping Mall on weekends to drink lattes, catch a movie or browse through the more than 80 stores.

Many questions

Police in Kenya grew irritated as people took to social media to describe what they were seeing and hearing.

"If you must Facebook or tweet, then talk about football or your favourite music but NOT MISINFORM the public on security operations!" authorities said on Twitter.

Three injured security forces were taken out of the besieged mall, but the severity of their injuries was unclear.

By Sunday afternoon, at least 1,000 people had been freed from the mall, Kenyatta said. But some 30 people were believed to still be held.

Later, that number fell to no more than 10, military spokesman Cyrus Oguna told CNN affiliate KTN.

"The number that is still left in the building is very, very small," he said, without providing details on how people got out.

One apparent hostage left the building Sunday, and said she had been hiding in the basement of the mall, 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 were at the scene and were working with their Kenyan counterparts in the hostage crisis, Kenyan government sources told CNN.

Kenyatta said several nations had offered help but "this remains an operation of the Kenya security agencies."

State House spokesman Manoah 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 terrorism 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."

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.

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.

A State Department spokeswoman said Sunday there were five Americans among the injured, but none among the dead.

"Obviously it's an enormous offense against everybody's sense of right and wrong," said Secretary of State John Kerry. "It represents the seriousness and the breadth of the challenge we face with ruthless and completely reckless terrorists, and we're going to pursue them."

The U.S. Embassy asked personnel to stay in place Sunday and avoid the Westgate Mall area and any large gatherings. All U.S. citizens in Kenya were 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.