The hotel says 138 people remain inside. The gunmen stormed it shooting and shouting “God is great!” in Arabic, eyewitnesses say.
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 US-owned hotel is popular with foreign businesses and airline crews.
There is as yet no established link with the attacks in Paris one week ago that killed 130 people.
The US Department of Defense told the BBC that US special forces were “currently assisting hostage recovery efforts”.
A US official said around 25 military personnel were in Bamako at the time of the attack and that some of them are helping “with moving civilians to secured locations, while Malian forces clear the hotel of hostile gunmen”.
Six Americans are reported to have been rescued.
France’s defence ministry says its special forces are also on site at the hotel.
The UN peacekeeping force said it was also 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.
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.
Algerian Foreign Minister Ramtane Lamamra was quoted by the state-run APS agency as saying seven Algerians staying at the hotel had been saved.
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.
THE PASHTUN TIMES