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.
- Two Belgians, including Geoffrey Dieudonne, an official at the parliament in Belgium's Wallonia region.
- Three Chinese, Zhou Tianxiang and Wang Xuanshang and Chang Xuehui were executives from the state-owned China Railway Construction Corp, the company said in a statement on its website.
- US national Anita Ashok Datar, 41, was in Mali working on projects involving family planning and HIV. Ms Datar, the mother of a 7-year-old boy, was a senior manager at Palladium Group, an international development organisation.
- Six Russians were killed, all employees of the Volga-Dnepr airline, the Russian foreign ministry said in a statement. Volga-Dnepr reported that the six were Stanislav Dumansky and Pavel Kudryavtsev, mechanics; Vladimir Kudryashov, a flight radio operator; Konstantin Preobrazhensky, a flight engineer; Sergey Yurasov, a load manager, and Aleksandr Kononenko, a navigator.
- Israeli education consultant and executive Shmuel Benalal, who is reported to have been in Mali to work with the government.
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.
At the scene: Thomas Fessy, BBC West Africa correspondent
Mali woke up to a state of emergency on Saturday morning but the streets of the capital are still bustling.
Perhaps the state of emergency does not make a difference for the people here as the whole country has been on edge for three years with jihadi threats coming from the north.
I drove through the city and I could not really tell that the presence of security forces had been stepped up.
There is a lot of anxiety at the entrances to some of the main hotels which host foreign guests. Visitors are being searched more thoroughly and, in some cases, cars are not allowed to park inside the hotel compound.
Staff from the hotel where I am staying even apologised for taking their time to look through our luggage despite knowing us well from previous trips.
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, our correspondent says.
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.
Militancy in Mali:
- October 2011: Ethnic Tuaregs launch rebellion after returning with arms from Libya
- March 2012: Army coup over government's handling of rebellion, a month later Tuareg and al-Qaeda-linked fighters seize control of north
- June 2012: Islamist groups capture Timbuktu, Kidal and Gao from Tuaregs, start to destroy Muslim shrines and manuscripts and impose Sharia
- January 2013: Islamist fighters capture a central town, raising fears they could reach Bamako. Mali requests French help
- July 2013: UN force, now totalling about 12,000, takes over responsibility for securing the north after Islamists routed from towns
- July 2014: France launches an operation in the Sahel to stem jihadist groups
- Attacks continue in northern desert area, blamed on Tuareg and Islamist groups
- 2015: Terror attacks in the capital, Bamako, and central Mali
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