Security forces surrounded the Splendid Hotel and were awaiting orders to begin an assault to rescue the hostages and retake the building, which is frequented by Westerners, the country's foreign minister Alpha Barry said in a telephone interview.
Medical personnel moved wounded away from the front of the hotel.
A US defense official said that France had requested US intelligence surveillance and reconnaissance support in the city and at least one US military member in Burkina Faso was giving "advice and assistance" to French forces at the hotel.
The government has not ruled out calling for help from French special forces stationed in the country, Barry said in a telephone interview.
This is the first time Islamist militants have carried out an assault in the capital of Burkina Faso.
It follows a deadly raid on a luxury hotel in Mali last November in which two attackers killed 20 people including citizens of Russia, China and the United States. There have been attacks by militants in other countries in West Africa.