Malian security forces are hunting three suspects connected to the attack on a hotel in the capital, Bamako, on Friday, in which 19 were killed.
Two militants were also killed, after special forces stormed the hotel, freeing dozens of trapped guests.
Al-Qaeda in the Islamic Maghreb and its affiliate, al-Murabitoun, said they carried out the attack.
President Ibrahim Boubacar Keita has declared a 10-day state of emergency and three days of national mourning.
But speaking outside the luxury Radisson Blu hotel a day after it was attacked the president said that the country remained open for business.
“Mali is not and will never be a closed border zone. Paris isn’t, Geneva isn’t, New York isn’t, Moscow isn’t,” he said.
Gunmen entered the hotel on Friday morning, shooting and driving their vehicle through a security barrier, one eyewitness said.
Most of the hotel guests and staff were freed hours later when Malian special forces, French special forces and off-duty US servicemen stormed the hotel to end the siege.
It is not clear if the suspects now being sought took part in the attack or were accomplices.
The exact number of gunmen is also not known. Eyewitnesses said up to 13 entered the hotel shooting, however the company that runs the hotel, Rezidor Group, said on Friday that only two attackers were involved.
A US national also died, and US President Barack Obama said the attack was yet another reminder that the “scourge of terrorism” threatened many nations.
UK Foreign Secretary Philip Hammond said three Britons who had been in the hotel were safe.
President Keita said Mali would “do everything to eradicate terrorism” in the country.
Seven Malians, including police officers and security guards, are currently being treated at Bamako’s Gabriel Toure, most of them for bullet wounds.
The claim by a Saharan jihadist group allied to al-Qaeda that they were behind the attack is a reminder that the country still faces an insurgency, says the BBC’s Frank Gardner.
In 2013, French forces managed to reverse the takeover of much of Mali by Islamist militants.
But it is a large country with porous borders and areas of ungoverned space in which jihadist groups have been able to hide and plan attacks.
It has not been helped by the ease with which weapons can come across from Libya, nor by the proximity of a murderous insurgency in Nigeria.
There is as yet no established link with the attacks in Paris one week ago that killed 130 people.
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.
The UN force in Mali took over responsibility for security in the country from French and African troops in July 2013, after the main towns in the north had been recaptured from the Islamist militants.