Nairobi, Kenya (CNN) -- Night fell Monday in Nairobi with no clear resolution of the standoff between Kenyan forces and terrorists at Westgate Shopping Mall.
Kenyan authorities sounded increasingly confident that they had brought the three-day standoff to a close with an assault Monday, reassuring a nervous public that there was little chance of escape for any surviving Al-Shabaab gunmen who had terrorized the mall, killing at least 62 people.
"Taken control of all the floors. We're not here to feed the attackers with pastries but to finish and punish them," Kenyan police Inspector General David Kimaiyo said on Twitter.
But Kenyan security forces suspect several gunmen remain inside the besieged mall in Nairobi, a senior Kenyan official said Monday night. A sweep of the complex was expected to continue Tuesday.
It wasn't clear Monday night whether any hostages remained inside the four-story mall. The Kenya Red Cross said 65 people were missing after the attack.
Gunfire echoed from the mall sporadically during the day, sending journalists and aid workers scrambling for cover. Thick heavy smoke -- from a fire set by terrorists, according to Kenyan authorities -- billowed into the air much of the afternoon.
Three terrorists have been confirmed killed since Saturday, the Interior Ministry said Monday. Eleven Kenyan soldiers have been wounded, according to the Kenya Defense Forces. More than 200 civilians have been rescued, the military said.
Away from the mall, Kenyan authorities said they had arrested more than 10 people for questioning in connection with the attack, including at least four taken into custody at an airport.
Authorities urged law enforcement officers to closely scrutinize travelers' documents, and the country's Immigration Department said in a tweet that it had increased security at entry and exit points.
Before its Twitter account was suspended, Al-Shabaab issued a list of the names of nine people it said were among the attackers. It said three were from the United States, two from Somalia and one each from Canada, Finland, Kenya and the United Kingdom. Sources within Al-Shabaab also told CNN that the nine names published on Twitter were among the alleged hostage-takers, but CNN has not been able to independently confirm that.
U.S. officials don't have any confirmation of Americans having been involved in the attack, Deputy National Security Adviser Ben Rhodes told reporters, and a senior U.S. official told CNN that Al-Shabaab's claim that Americans were among its ranks of attackers at Westgate seemed less solid.
Intelligence analysts are poring over electronic intercepts in an effort to verify the terror group's claims, two law enforcement sources told CNN.
The FBI also was looking into the claims but has not yet confirmed them, law enforcement officials told CNN.
"At this point we have no definitive evidence of the nationalities or identities of the perpetrators," State Department spokeswoman Jen Psaki said Monday.
In the past, federal officials and Somali-American leaders in Minneapolis have reported that Al-Shabaab has recruited young men there to go to Africa to fight.
U.S. President Barack Obama expressed condolences over the attack after a meeting on the sidelines of the U.N. General Assembly Monday. He didn't specify whether Americans had been involved, but he pledged U.S. support and described the situation as a matter of global concern.
"This, I think, underscores the degree to which all of us as an international community have to stand against the kind of senseless violence that these kinds of groups represent," Obama said.
The terrorist attack began at midday Saturday, Nairobi time, with an estimated 10 to 15 gunmen taking over the mall in what hospital volunteer Abiti Shah said witnesses told her was "like a Hollywood action scene."
"They just started firing in the air," Shah said, retelling the witness accounts.
A youth cooking competition was taking place at the mall at the time, and terrified shoppers fled for their lives as gunfire echoed through the building.
Witnesses said the gunmen went from store to store, shooting people, and then took hostages.
Survivor Bendita Malakia, a North Carolina woman who moved to Nairobi in July, told CNN affiliate WAVY that she took refuge behind the closed metal gates of a store with dozens of others.
"While we were back there, you could hear them methodically going from store to store, talking to people and asking questions," she said. "They were shooting, screaming. Then it would stop for a while and they would go to another store."
Al-Shabaab has claimed that the attackers targeted non-Muslims and vowed they would not negotiate for the hostages' lives. CNN security analyst Peter Bergen said the terrorists apparently took hostages only to prolong the siege and win more media attention.
Most of the dead were said to be Kenyans.
Six British citizens, two French nationals, two Indians and two Canadians, including a diplomat, also died, their governments said.
Those killed include:
• Elif Yavuz, a senior vaccines researcher for the Clinton Health Access Initiative based in Tanzania. Yavuz, a Dutch national, was pregnant and expecting her first child in October, according to Julio Frenk, dean of faculty at the Harvard School of Public Health. "Elif was brilliant, dedicated, and deeply admired by her colleagues, who will miss her terribly," the Clinton family said in a statement. The Dutch Foreign Affairs Ministry confirmed a 33-year-old Dutch woman had been killed.
• A major African poet, author and Ghanian statesman, Kofi Awoonor, Ghana's president said. Awoonor received his Ph.D. from New York's Stony Brook University and was a professor of literature there in the 1970s.
• The nephew of Kenyan President Uhuru Kenyatta and the man's fiancee.
• A Peruvian doctor, Juan Jesus Ortiz, who had previously worked for the United Nations Fund for Children and lived in Kenya doing consulting work, the country's Foreign Affairs Ministry said.
• Sridhar Natarajan, 40, an Indian national and employee of a local pharmaceutical firm, and 8-year-old Paramshu Jain, the son of a bank branch manager, CNN sister network CNN-IBN reported, citing government officials in New Delhi.
Kenyatta said more than 175 people had been wounded. Five were Americans, the State Department said Sunday.
Elaine Dang, 26, a University of California, Berkeley, graduate from San Diego, underwent surgery to her chest, arms and legs.
"I'm OK, I'm very grateful to be alive," she told CNN affiliate KFMB-TV
She said two friends died in the attack.
The Somalia-based Al-Shabaab terror group had said on Twitter that it had sent the gunmen to the mall in retaliation for Kenya's involvement in an African Union military effort against the group, which is al Qaeda's proxy in Somalia.
Last year, the Kenyan military was part of a peacekeeping force that defeated Al-Shabaab forces to liberate the key Somali port of Kismayo.
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.
The mall attack is the deadliest terror attack in Kenya since al Qaeda blew up the U.S. Embassy there in 1998, killing 213 people.
On Monday, Kenya's foreign minister told CNN it's clear that Al-Shabaab was not acting alone.
"This bares the hallmarks of al Qaeda. This is not just Al-Shabaab. In fact, the leaders are not Somali, as you may have heard. This was al Qaeda. It was a very well-coordinated effort, it was very well planned," Kenyan Foreign Minister Amina Mohamed said.
But the attackers' national origins are irrelevant, she said.
"It doesn't matter where they come from. There are some Americans. There are some Brits. There are some others. It has nothing to do with the nationality of people," Mohamed said. "They are all evil and we must deal with them as such."
Reports of a white woman among the terrorists inside the mall were the subject of contradictory accounts Monday.
Senior Kenyan intelligence officials told CNN that surveillance video from inside the mall appears to show such a woman taking part in the attack. Analysts believe she is British, the sources said.
But Kenyan Interior Minister Joseph Ole Lenku told reporters that all of the attackers were men. Some of them apparently had dressed as women, he said.
The reports came after earlier speculation that the Al-Shabaab-affiliated "White Widow," Samantha Lewthwaite, may have been involved in the Westgate attack.
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.
State House spokesman Manoah Esipisu earlier said that "nothing is being ruled out" when it comes to Lewthwaite's possible involvement.
Such involvement would be "very unusual," said Bergen, the security analyst.
"Typically these groups are misogynist," he said. "Their view is the woman should be in a home and shrouded in a body veil."
Lenku said that Monday's effort to roust the terrorists was a Kenyan operation, but government sources told CNN that Israeli special forces also were at the scene.
Kenyatta, the Kenyan president, vowed Sunday to punish those responsible for the attacks.
"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," he said.
U.S. Secretary of State John Kerry promised an American investigation.
"Obviously, it's an enormous offense against everybody's sense of right and wrong," Kerry said. "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."