Although all civilians have been evacuated from the hotel , special forces were still trying to dislodge the gunmen from the upper floors. Two gunmen were killed in the siege.
The attackers no longer have hostages with them. They are dug in in the upper floors, spokesman Amadou Sangho said.
An al-Qaida affiliated group Al-Mourabitoun claimed responsibility for the attack.
The group, based in northern Mali, is led by Mokhtar Belmokhtar who was behind the deadly attack on a gas plant in Algeria in 2013.
Ban Ki-moon, the UN secretary general, condemned the attack
UN peacekeepers said they counted 12 bodies in the basement of the hotel and another 15 on the second floor, a UN official told Reuters on condition of anonymity adding that UN troops were still helping Malian authorities search the hotel.
Geoffrey Dieudonne, an official with the parliament of Belgium’s French-speaking community, had been in Mali along with others for a convention, the parliament said in a statement without elaborating.
Two gunmen were killed in the hotel siege. The gunmen are holding no more hostages, Mali’s security minister confirmed.
Malian special forces stormed the luxury hotel after Islamist gunmen took 170 people, including many foreigners, hostage in the capital of the former French colony which has been battling rebels allied to al Qaeda for several years.
A senior security source said gunmen burst into Radisson Blu hotel at 7 am (0700 GMT), firing and shouting “Allahu Akbar”, or “God is great” in Arabic, and began working their way through the building, room by room and floor by floor.
Some of the hostages escaped under their own steam while a few others were freed after showing they could recite verses from the Quran, one security source said.
Twelve Air France flight crew were in the hotel, but all were extracted safely, the French national carrier said.
A Turkish official said three of six Turkish Airlines staff who had been in the hotel managed to flee.
Among those trapped were several Chinese tourists.
Malian President Ibrahim Boubacar Keita cut short a trip to a regional summit in Chad to return to Bamako, his office said.
The raid on the hotel, which lies just west of the city centre near government ministries and diplomatic offices, comes a week after Islamic State militants killed 129 people in Paris.
A paramedic said three security guards had been wounded, including one who was in a critical condition after being shot. AFP’s correspondent saw a police officer, who had also been shot, being evacuated by security forces.
Two freed female hostages — a Turkish aviation worker and an Ivorian woman who was at the hotel for an economic conference — told AFP they saw the body of a fair-skinned man lying on the floor of the hotel.
Earlier, the Rezidor Hotel Group, the US-based parent company of Radisson Blu, said there were a total of 170 hostages — 140 guests and 30 employees.
A gardener at the hotel told BBC that he was sweeping the yard around 7 am when a gang of masked gunmen arrived in a car with a diplomatic license plate. When the three guards stopped them at the hotel gate, they started firing.
The head of security confirmed three security guards posted at the gate of the hotel were injured in the assault.
A staffer at the Radisson Blu hotel who gave his name as Tamba Diarra said over the phone that the attackers used grenades in the assault.
Speaking to Al Jazeera channel by phone from Bamako, business owner Garba Konate said about 10 gunmen arrived early in the morning and shot at the guards in front of the Radisson.
Another witness said he helped a wounded guard to safety.
“I started hearing gunshots coming from the hotel,” said Ibrahim, 28, who works at a cultural center 40 meters away.
“Soon after, I saw one of the guards running out, injured… The security guard told me the shooters were so quick that he doesn’t even know how many came in,” he told the channel.
A French consultant, who stays regularly at the hotel, described it as “an obvious target for terrorists”.
“The Radisson is at a crossroads, one of the roads was blocked. Security is provided by private guards. They passed a metal detector under cars,” said the consultant, who spoke on condition of anonymity.
“I noticed that when they knew you, they didn’t (use the metal detector) any more.”
The US Embassy tweeted that it was “aware of an ongoing active shooter operation at the Radisson Hotel,” and instructed its citizens to stay indoors.
An Islamist group had claimed responsibility for the death of five people last March in an attack on a restaurant in Bamako.
Islamist groups have continued to wage attacks in Mali despite a June peace deal between former Tuareg rebels in the country’s north and rival pro-government armed groups.
In mid-2012 the north fell under the control of jihadist groups linked to Al-Qaeda. They supplanted Tuareg rebels and imposed a brutal interpretation of sharia law on the region, with Bamako reeling from a military coup.
The Islamists were largely ousted from towns by an ongoing French-led military operation launched in January 2013, but they have since launched sporadic attacks on security forces from desert hideouts.
Despite the peace deal, large swathes of Mali remain beyond the control of government and foreign forces.
In a recording authenticated by Malian authorities this week, a jihadist leader in Mali denounced the peace deal and called for further attacks against France, which is helping national forces fight extremists.