Armed men attacked the Grand Mosque in Salmossi on Friday evening, a source told AFP, adding that 13 died on the spot and three succumbed to their injuries later.
Two of the wounded are in critical condition, the source added.
A resident from the nearby town of Gorom-Gorom confirmed the attack, saying Salmossi residents had fled their homes afterwards.
Although hit by jihadist violence, many Burkinabes oppose the presence of foreign troops -- notably from former colonial ruler France -- on their territory.
On Saturday, about a thousand-strong crowd marched in the capital Ouagadougou, "to denounce terrorism and the presence of foreign military bases in Africa."
"Terrorism has now become an ideal pretext for installing foreign military bases in our country," said Gabin Korbeogo, one of co-organisers of the march.
"The French, American, Canadian, German and other armies have set foot in our sub-region, saying they want to fight terrorism. But despite this massive presence... the terrorist groups... are growing stronger."
Until 2015, landlocked Burkina Faso was largely spared violence that hit Mali and then Niger, its neighbours to the north.
But jihadists -- some linked to Al-Qaeda, others to the so-called Islamic State group -- started infiltrating the north, then the east, and then endangered its southern and western borders.
Combining guerrilla hit-and-run tactics with road mines and suicide bombings, the insurgents have killed nearly 600 people, according to a toll compiled by AFP. Civil society groups put the tally at more than 1,000.
Around 300,000 people have fled their homes and almost 3,000 schools have closed. The impact on an overwhelmingly rural economy is escalating, disrupting trade and markets.
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