The drama saw Burkinabe troops, backed by French special forces, battle militants who stormed the four-star Splendid Hotel, which is popular with foreigners and United Nations staff.
At least 13 foreigners are among the dead, according to a government toll.
Burkina Faso has declared three days of national mourning following the onslaught, which echoed another Al-Qaeda attack last year on a luxury hotel in neighbouring Mali where 20 people were killed, mostly foreigners.
It is still not clear how many attackers took part in the onslaught - the bodies of three have been identified, but some witnesses reported seeing more.
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Burkina Faso's Interior Minister Simon Compaore said search security forces were carrying out careful searches, while at the scene of the attack a security cordon was widened today.
Investigators wearing white protective gloves were seen in the streets around the Splendid and the Cappuccino cafe, which was also attacked.
Until recently Burkina Faso had largely escaped the tide of Islamist violence spreading in the restive Sahel region and the hotel assault will heighten fears that jihadist groups are casting their net wider in search of targets in west Africa.
President Roch Marc Christian Kabore, who took office just last month, said Saturday that the country was in shock.
"For the first time in its history, our country has fallen victim to a series of barbaric terrorist attacks," he said, adding that the people of Burkina would nevertheless "emerge victorious".
The hotel and surrounding area became a battleground as Burkina Faso troops, backed by French forces based in the city under a regional counterterrorism initiative, launched an attempt to retake the hotel around 2:00 am (local time).
Among those killed were six Canadians, two French nationals, two Swiss, an American, a Portuguese and a Dutch person, according to the prosecutor's office.