An attack by suspected Islamist militants who took 170 people hostage at Radisson Blue Hotel in the Malian capital is over, US officials say.
The National Security Council condemned the “heinous attack” in Bamako.
Mali said the gunmen had “no more hostages” and were being chased. More than 20 people died, and a national state of emergency has been declared.
Al-Qaeda in the Islamic Maghreb and its offshoot al-Murabitoun said they carried out the attack.
Speaking after a crisis cabinet meeting late on Friday, Malian President Ibrahim Boubacar Keita announced the state of emergency from midnight on Friday for 10 days, as well as three days of national mourning.
He said 21 people were killed in the attack, including two gunmen.
Earlier reports said at least 27 people had died. A UN official, who spoke on condition of anonymity, said 12 bodies were found in the basement and 15 on the second floor.
One of the hostages killed was Geoffrey Dieudonne, a member of parliament in Belgium’s Wallonia region.
China’s state news agency Xinhua says three Chinese nationals are among the dead.
The US state department said one US citizen was killed. She was named as Anita Datar, 41, senior manager at an international development company and a former aid worker.
UK Foreign Secretary Philip Hammond said three Britons in the hotel were safe.
Pictures showed that some of the hostages leaving the hotel were wounded.
US President Barack Obama said the attack was yet another reminder that the “scourge of terrorism” threatened many nations.
He said the barbarity of the assault “only stiffens our resolve to meet this challenge”.
The US-owned hotel is popular with foreign businesses and airline crews.
Eyewitnesses said up to 13 gunmen had entered the hotel shooting and shouting “God is greatest!” in Arabic.
Analysis: BBC Security Correspondent Frank Gardner
The claim by an obscure Saharan jihadist group allied to al-Qaeda that they were behind the attack is a reminder that the country still faces an insurgency.
In 2013 French forces effected a stunningly swift reversal of al-Qaeda’s takeover of most of Mali. But Mali is a large, poor country with porous borders and large areas of ungoverned space where 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 where Boko Haram reportedly killed more people last year than Islamic State did in Syria and Iraq.
It is clear that Mali will continue to need international military support. But to defeat terrorism in the long term it will also need secure borders, good governance and more economic opportunities for young Malians.
Before special forces stormed the building, a security source told Reuters news agency that some hostages who were able to recite verses of the Koran were being freed.
Mali’s presidency thanked the security forces and friendly countries for their support in responding to the attacks.
Off-duty US servicemen helped in the hostage rescue operation. French special forces were also involved.
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.
Mali’s President Ibrahim Boubacar Keita cut short a trip to a regional summit in Chad.
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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