Shots were heard late Sunday near Kabore's home after soldiers staged mutinies at several barracks to demand the sacking of the country's military top brass and more resources for the battle against extremist groups.
Residents also reported they saw a helicopter above the president's home in the capital of Ouagadougou.
It followed gunfire earlier Sunday at several army bases, prompting fears of yet another coup in a volatile West African country prone to military takeovers.
But the government quickly denied rumors of a putsch, and a list of demands presented by the rebellious troops made no mention of trying to oust Kabore while emphasizing the need for a better anti-extremist strategy.
"We want adequate resources for the battle" against extremists, a soldier from the Sangoule Lamizana base in Ouagadougou said in a voice recording received by AFP.
The disaffected soldiers also wanted top generals to be "replaced", better care for wounded troops, and more support for the families of soldiers killed in battle, the spokesman for the mutinous troops added in the anonymous recording.
RHM/PR