Al-Qaeda faction from the country's restive north had earlier claimed responsibility for the nine-hour hostage-taking siege that ended after special forces stormed the luxury hotel.
"We are actively pursuing three suspects who might have been involved in Friday's attack on the Radisson Blu hotel," a Malian security official told the AFP news agency.
Mali was under a state of emergency on Saturday and three days of mourning were announced by President Ibrahim Boubacar Keita, who also clarified the death toll after Malian state television reported late Friday that 27 were dead, along with three attackers.
"This evening, the death toll is heavy and terrible: 21 dead, two [assailants] amongst them, and seven wounded," Keita said.
Friday's assault on the Radisson Blu hotel was the latest in a series of deadly raids this year on high-profile targets in Mali, which has battled various rebel groups based in its desert north for years.
The attack is a sharp setback for former colonial power France, which has stationed 3,500 troops in northern Mali to try to restore stability.
"There's a real sense of grief here - how could this have happened?" Al Jazeera's Nicolas Haque reported from outside the hotel on Saturday.
"People here didn't expect such a brazen attack. It's one of the most secure areas in Bamako. It comes as a shock as the attackers literally walked into the hotel."
Malian, French and US security forces ended the siege after the gunmen stormed the hotel and took about 170 people hostage.
The US State Department said one American was among the dead. US special forces helped rescue at least six others, a military spokesman told reporters in Washington.
President Barack Obama said on Saturday the United States was trying to account for all its citizens at the hotel as he denounced the assault.
"This barbarity only stiffens our resolve to meet these challenges," he said from a summit in Malaysia. "The United States will be relentless against those who target our citizens."
Gunmen shouting "Allahu Akbar", or "God is great", opened fire outside the hotel in the centre of the capital before rushing inside.
Al-Mourabitoun, an armed group that has had ties to al-Qaeda, claimed responsibility for the attack, saying it carried it out "in coordination with Imarat al-Sahra group and al-Qaeda in the Islamic Maghreb [AQIM]".
Several Russian nationals were killed in Friday's attack, foreign ministry spokeswoman Maria Zakharova told Russian news agencies on Saturday.
President Vladimir Putin said "the widest international cooperation" was needed to confront global terrorism, the Kremlin said in a statement.
Al-Mourabitoun, in a recording obtained by Al Jazeera, said it would only release the hostages it had taken when its members were freed from Bamako's prisons, and when what it called "aggression against the people of northern Mali" is stopped.
