The gunmen stormed the US-owned hotel, which is popular with foreign businesses and airline crews, shooting and shouting “God is great!” in Arabic.
Malian officials said 30 hostages have been freed. State TV earlier put the figure at 80.
Three people have been shot dead and two soldiers wounded, officials say.
Interior Minister Salif Traore said the soldiers’ lives were not in danger.
The Radisson Blu hotel group has set up special phone lines for families who may have been affected. It says 125 guests and 13 staff are still in the building.
Air France says 12 of its crew have been successfully freed in the rescue operation; Turkish Airlines says five of its crew are out, but two remain in the hotel.
Twenty Indian nationals are in part of the hotel but are safe, according the Indian embassy in Mali, while Chinese state TV reported four of 10 Chinese citizens caught up in the attack had been rescued.
The UN peacekeeping force said it was supporting the operation as Malian special forces freed hostages “floor by floor”.
“We have sealed all the exit points of the hotel, so be assured none of the hostage takers will be able to escape,” the interior minister told reporters outside the Radisson Blu.
An Ivorian guest said she and six other people were escorted out by security forces as the gunmen rushed “toward the fifth or sixth floor”.
“I don’t know where to go. I’m tired and in a state of shock,” Monique Kouame Affoue Ekonde told the AP news agency.
Earlier, a security source told Reuters that some hostages who were able to recite verses of the Koran were being freed.
In August, suspected Islamist gunmen killed 13 people, including five UN workers, during a hostage siege at a hotel in the central Malian town of Sevare.
France, the former colonial power in Mali, intervened in the country in January 2013 when al-Qaeda-linked militants threatened to march on Bamako after taking control of the north of the country.
BBC Monitoring’s Africa security correspondent Tomi Oladipo says the attack comes just days after Iyad Ag Ghaly, the leader of the Islamist militant group Ansar Dine, called for attacks on France and its interests in Mali.
His al-Qaeda-linked group was among those ousted from northern towns in 2013.
Source BBC
Mali forces storm hostage hotel
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Malian special forces have entered the Radisson Blu Hotel in Mali’s capital, Bamako, to end a siege by gunmen. The hotel says 138 people remain inside.