Gunfire was no longer heard about an hour after the soldiers attacked, an RTB reporter at the scene said, but authorities did not immediately say if the siege had ended.
At least 20 people were wounded, RTB said. There were no immediate details about deaths but several bodies were seen outside the hotel, Burkinabe police said.
About 15 hostages were freed by security forces, RTB reported, including the country's public sector minister.
Al Qaeda in the Islamic Maghreb immediately claimed credit for the assault that had similarities to a November hotel attack in nearby Mali that left 22 dead, reported a Mauritania-based news agency. CNN could not independently confirm that claim.
The violence started Friday night when an undetermined number of gunmen stormed the Cappuccino café-restaurant while about 100 people were inside, the owner told RTB.
The gunmen next invaded the hotel across the street, took hostages and exchanged fire with security forces, the gendarmerie said, according to RTB. The hotel is a favorite of Western diplomats and business people.
Witnesses said the attackers wore turbans, were "light-skinned" and spoke a language not native to Burkina Faso, a former French colony in West Africa.
Burkinabe security forces, with support from American and French troops, circled the hotel for several hours before attacking.
At least one U.S. soldier was on the scene, a U.S. defense official told CNN. France requested immediate support from U.S. soldiers and a U.S. drone will be flown over the scene to provide surveillance, the official said.
Al Qaeda group claims responsibility
The attack was executed by the Islamist militant group Al-Mourabitoun group, led by veteran al Qaeda figure Mokhtar Belmokhtar,
al Qaeda in the Islamic Maghreb said, according to the Mauritania-based Al Akhbar news agency. The interim Libyan government reported last June that an American airstrike had killed Belmokhtar.
Al-Mourabitoun had claimed credit for an attack at the Radisson Blu Hotel in neighboring Mali in late November
that left 22 people dead, according to the U.N. mission in Mali.
The United States has approximately 75 military personnel in Burkina Faso, including 15 assigned to the U.S. Embassy and about 60 who provide security assistance -- training, advising and assisting -- to the French military in Burkina Faso, the senior U.S. defense official told CNN.
The U.S. Embassy in Ouagadougou said via Twitter that it is aware of the situation. There was no indication if there are any Americans inside the hotel. In a tweet, the embassy urged U.S. citizens to avoid downtown Ouagadougou.
The U.S. defense official said reports U.S. military people were sheltering in the hotel were false.
A U.N. spokesman in Ouagadougou, Emile Kabore, told CNN he does not believe any U.N. staffers are staying at the hotel, which is often visited by U.N. personnel in West Africa.
Burkina Faso elected new president in November
An Air France flight from Paris to Ouagadougou has been re-routed to Niamey, Niger, since the attack, French Ambassador to Burkina Faso Gilles Thibault said via Twitter late Friday.
The announcement followed the decision by Burkinabe authorities to adjust the curfew in Ouagadougou. The curfew is now from 11 p.m. to 6 a.m. The previous curfew was from 1 a.m. to 6 a.m. and was put in place last year.
A French Embassy spokesman told CNN the embassydid not know if any French nationals were inside the hotel at the time of the attack.
In November, Burkina Faso elected a new president
after nearly three decades of autocratic rule followed by a civil uprising.
Roch Marc Christian Kabore won more than 53% of votes. Kabore was a former prime minister of the West African nation.
The West, particularly France, considers Burkina Faso a key ally in the fight against al Qaeda. The country was formerly known as the Republic of Upper Volta, when it was established in 1958 as a self-governing colony under France.
Blaise Compaore served as President from 1987 until he resigned in 2014.
Elections in October were postponed because of a failed coup against a transitional government. Kabore was elected in November.