The attack, conducted by at least two people, began in Mali's capital city of Bamako, with gunmen storming the building. The United Nations reported Friday at least 27 were killed, including the two attackers, though Mali's government reduced that number Saturday.
U.S. officials were still trying to account for other Americans "who may have been at the hotel," President Obama said.
The president called the attack "appalling" and extended his condolences to the family of the American killed, Anita Datar, 41, vowing to be "relentless" in pursuing those responsible.
"On behalf of the American people I want to extend our deepest condolences to the people of Mali and the victims and families, including at least one American," he said. "These were innocent people who had everything to live for, and they’ll be remembered for the joy and love that they brought to the world."
A family member said Datar was in Mali "doing what she loved -- strengthening public health."
"She dedicated her life to her work," the family member said.
Datar was a founding board member of the non-profit Tulalens, which aims to "connect under-served communities to quality health services to improve lives," the group's website says.
According to her biography on the site, she was a Peace Corps volunteer in Senegal the late 1990s, went to school for public health and had a decade of experience in HIV policy.
Mali has declared a 10-day state of emergency in the wake of the attack. The U.S. Embassy in Bamako has lifted its "shelter in place," but still urges Americans to limit their movement around the city and be vigilant.
Two attackers died in the incident, said Olivier Salgado of the United Nations Stabilization Mission in Mali, though the total number of attackers was not immediately clear.
"They came to kill, not to take hostages.”
A Belgian member of Parliament, Geoffrey Dieudonné, was among those killed, Belgium’s regional Parliament said. Dieudonné was training officials from Mali’s Parliament. The Parliament said the precise circumstances of his death are not yet known.
Three Americans made several trips into the hotel to help save others who were trapped, according to a U.S. government official.
A State Department Diplomatic Security Special Agent was near the hotel when he learned of the attack and rushed to the scene, according to a U.S. Government official, where he met up with two Department of Defense personnel who were part of the State Department Chief of Mission Staff.
A first-floor room was on fire when the trio arrived and the halls were filling with smoke. After getting in touch with the U.S. Embassy, the three learned that several U.S. State Department personnel were trapped inside the building and one was believed to be near the burning room, said the U.S. official.
The Americans went into the hotel, according to the U.S. official, but could not see through the smoke. They called out to a trapped person on the first floor, and in the darkness, they pulled him to safety, said the U.S. official.
The three Americans went back into the building several times to remove trapped Americans who were part of the Chief of Mission staff, the official said, adding that all Chief of Mission personnel are safe and accounted for. They were armed but never fired, according to the official.
There were 22 military and civilian U.S. Defense Department personnel in Bamako, including five at the hotel at the time of the attack, according to a defense official. Everyone was accounted for and there were no reports of injuries, the official said.
Some of the five U.S. military personnel in the hotel, including civilians and service-members, hid and avoided being seized by the gunmen, a defense official said.
One U.S. servicemember outside the hotel stepped in to help first responders move civilians from the hotel to secure locations, as Malian forces worked to clear the hotel of hostile gunmen, the defense official said, adding that U.S. forces did not directly participate in the operation.
Another U.S. servicemember helped at the Joint Operations Center, which was set up to respond to the attack.
Six U.S. citizens were rescued from the hotel, according to the U.S. Africa Command.
National Security Council spokesman Ned Price said the U.S. is continuing to coordinate with U.S officials to verify the location of all American citizens in Mali.
Price said the U.S. stands with Mali "and others in the region fighting the terrorist groups that seek to undermine Mali’s efforts to build a durable peace following the crisis in 2012 and 2013." Price said the U.S. is prepared to help Mali investigate "this tragic terrorist attack."
The hotel said in a statement, "Our highest concern is the safety of all our guests and employees in the hotel. We are in constant contact with the authorities there and will share further information with you when we have it."
Radisson Blu receptionist Tambacouye Diarra told ABC News that he was at the reception desk surrounded by special forces. He said the gunmen were also surrounded by special forces in the hotel.
A gunman shot in his direction approximately 10 times, Diarra said. He said a gunman ran after him, but he was able to escape. Diarra said he saw people getting shot and some injured people being evacuated out of the hotel.
Among those in the hotel were three U.N. personnel, who are now safe, according to Salgado, and Air France and Turkish Airlines crew members, who are also safe, according to the airlines.
France, the former colonial power in Mali, launched airstrikes in Mali two years ago to prevent the establishment of a terrorist state after armed groups linked to al Qaeda took over vast stretches of Mali. French involvement in Mali eventually morphed into a larger operation that involved ground troops and French special forces. At its height, 4,000 French soldiers were largely successful in helping Mali push the al Qaeda-linked rebels out of the country.
ABC News' Jack Date and Ali Ehrlich contributed to this report.