Petro said Colombian security forces were not responsible but gave no further information about the bodies.
"I didn't give that order," Petro said on X after suggesting on Monday night that Ecuador had bombed Colombian territory.
Earlier on Tuesday, Noboa posted on X: "President Petro, your declarations are false, we are acting in our territory, not yours."
Noboa said the bombed locations were hideouts for mostly Colombian narco-terrorism groups.
"We will continue to clean up and rebuild Ecuador," he added.
The Ecuadorian government did not immediately respond to a request for comment regarding the remains.
Ecuador launched operations on Sunday night against criminal gangs in four provinces, as well as the border, but has not reported on operations at the border.
Ecuador has said its anti-drug trafficking operations are supported by allied countries, including the United States.
Petro later reposted an image from Colombian state-run RTVC television it said showed one of the bombs - a dark green cylinder lying in foliage.
The social media exchanges were the latest friction between Noboa and Petro, who have also argued over tariffs.
Noboa raised duties on Colombian goods to 50 per cent last month, claiming his neighbour was not doing enough to fight drug trafficking, and Colombia said it was considering a reciprocal measure.
