Speaking to reporters at the United Nations, Obama said, "We are providing all the cooperation we can." The terror group taking responsibility has claimed some of the attackers were Americans, and officials said five of the wounded were from the United States.
"I want to express my condolences not only to President [Uhuru] Kenyatta but to the Kenyan people," Obama said.
Obama said the United States would provide law enforcement help.
Fires set by gunmen inside Nairobi's Westgate Mall were brought under control Monday as Kenyan authorities secured the building where at least 62 people died.
The Interior Ministry said security forces have "dominated all floors of Westgate Mall" and troops are now concentrating on clearing the building of the gunmen who had slaughtered dozens of people in an attack that began Saturday.
The Interior Ministry, reporting on Twitter, said three gunmen were killed and others were injured.
Eleven members of Kenya's security force were injured and being treated at Defense Forces Memorial Hospital, officials said.
Several people were arrested at Nairobi's airport for questioning, the Interior Ministry said. Security has been increased at entry and exit points across the country.
The Kenya Red Cross, which earlier set the death toll at 69, said 62 people had died in the assault by Somalia-based al-Shabaab militants. The humanitarian agency said on its Twitter page some bodies had been double-counted as they were being moved between morgues. The Interior Ministry confirmed the death toll and said more than 200 civilians were rescued from the building, with 65 receiving treatment in various hospitals.
It wasn't clear whether any hostages remained in the mall.
If there were hostages, the number would be "very, very minimal," Interior Minister Joseph Ole Lenku said earlier Monday at a news briefing.
Most had been evacuated, he said.
Dark smoke rising from the building was from fires started by the gunmen as a distraction, Lenku said. The fires were brought under control by firefighters from various agencies, officials said.
The Interior Ministry said all exits from the building were barricaded, making it unlikely that any of the remaining gunmen would escape.
"We are in charge of the situation; our people are safe," Lenku said.
Before the assault, the militants were thought to have 10 hostages on one level of the mall, security officials said.
The FBI was looking into al-Shabaab's claims U.S. citizens participated in the attack but had not confirmed the allegations, law enforcement officials told CNN.
The mass shootings occurred Saturday with an estimated 10 to 15 gunmen going from store to store shooting people before taking hostages, witnesses said. Two attackers were killed the first day.
Most of the dead reportedly were Kenyans, including a family member of Kenyatta, who said he lost a nephew and the man's fiancee in the attack.
"These are young, lovely people I personally knew and loved," Kenyatta said. "Many of us have lost loved ones. Let us mourn them all as one nation and keep them always in remembrance and prayer."
African poet, author and Ghanian statesman Kofi Awoonor also was killed, Ghana's president said.
Four British citizens, two French nationals, two Canadians, including a diplomat, and a 33-year-old Dutch woman were killed, their governments said.
Kenyatta said five Americans were among the wounded.
Al-Shabaab leaders said the militants sought retribution for Kenyan military activity in Somalia, where Kenyan troops have driven al-Shabaab fighters out of much of the territory they once controlled.
Before its Twitter account was suspended, al-Shabaab posted a list of nine names it said were among the attackers, CNN reported. Militant leaders said three attackers were from the United States, two from Somalia and one each from Canada, Finland, Kenya and Britain.
Although they hadn't verified the al-Shabaab claims, authorities said they were growing more certain that U.S. citizens may have been involved. Federal officials and Somali-American leaders in Minneapolis reported al-Shabaab has recruited young men there, CNN said.
"[The attackers] 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 Sunday.
U.S. Secretary of State John Kerry promised an 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."
Obama called Kenyatta Sunday to reaffirm the "strong and historic partnership between the United States and Kenya," the White House said.
Observers say U.S.-Kenya relations have been strained since Kenyatta was elected.
The assault on the luxury mall popular with Westerners and Kenya's new consumer class is the deadliest terrorist attack in the country since al-Qaida operatives masterminded bombings of the U.S. embassies in Nairobi and Dar es Salaam, Tanzania, Aug. 7, 1998. The Nairobi blast killed 212 people and wounded an estimated 4,000. The Dar es Salaam attack killed 11 and wounded 85.
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