The strike yesterday came as Niger takes part in a regional offensive against Nigeria-based Boko Haram fighters, who have extended their brutal six-year insurgency to Niger, Chad and Cameroon.
A Niger army report obtained by AFP that gave the death toll said the plane's "origins remained undetermined."
"The victims were residents attending a mourning ceremony for a prefecture official," said a humanitarian source, who added that the attack was near the mosque in Abadam.
Meanwhile seven villagers in far north Cameroon were killed yesterday when battling Boko Haram fighters who stole 70 cows and torched houses in Gaboua.
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Nine Islamist militants also died in the clashes against the locals, armed with clubs, machetes and bows and arrows.
A spokesman for Nigeria's air force, Air Commodore Dele Alonge, denied all responsibilty for the 36 deaths in Abadam.
"It's not to my knowledge and there has not been any report from our people of such an incident," he said.
However, at least one local leader blamed Nigeria.
The leader said a similar air strike several days ago on the nearby village of Gamgara killed one person.