Various reports suggest that four attackers have been killed at the French embassy and three have been killed at the army headquarters.
Burkina Faso police have given an initial death toll of six attackers and seven security personnel, with another six people wounded, including two civilians.
Five members of the security forces were killed at the offices of the army chief of staff, while two others were killed at the nearby French Embassy, Radio Omega said, quoting government spokesman Remis Dandjinou.
Three security sources, two in France and one in West Africa, told AFP that at least 28 people were killed in the attack on the military headquarters alone. Guterres is closely watching and following the events and asked the special representative for West Africa and the Sahel, Mohammed Ibn Chambas, to travel to Burkina Faso as soon as possible.
But experts say the terror threat in Burkina Faso is increasingly homegrown.
The attack on the embassy and the French institute in Ouagadougou was ongoing, the French embassy said on its website, without giving further details.
The city's military headquarters and the embassy - which is also near the prime minister's office - are about one kilometre apart.
Mahamadou Issoufou, Niger's president and the current chair of the group, said Friday's attacks "will only strengthen the resolve of the G5-Sahel and its allies in the fight against terrorism".
French government sources said there were no French casualties and described the situation in Ouagadougou as "under control". They then ran towards the French embassy, according to witnesses who saw the attack from the state television offices facing the embassy. No French casualties were reported.
Responsibility for that attack was claimed by the jihadist group al Qaeda in the Islamic Maghreb.
Barricades were erected to keep people from that area and from the French Embassy and the prime minister's office in the eastern part of the city center where gunfire and smoke were reported.
In August 2017, an attack on a restaurant in Ouagadougou left 18 people dead.
Burkina Faso's communications minister says four Islamic extremists have been killed after they attacked the French Embassy in Ouagadougou, the capital. The 5,000-member force combines troops from Burkina Faso, Mali, Niger, Chad and Mauritania, with France leading the efforts to bring in worldwide funding.