The children have been missing since May 1, when the plane they were travelling in crashed in a thick jungle.
On Wednesday (May 17), Petro said in the now-deleted Twitter message that the children, aged 13, 9 and 4, as well as an 11-month-old baby, had been found alive thanks to arduous searching by members of the armed forces.
"I have decided to delete the tweet because it hasn't been possible to confirm the information provided by the (child welfare agency)," he said, adding that searches were ongoing.
"I'm sorry it happened," he said. "At this time there's no other priority other than moving forward with the search until you find them. The children's lives are the most important."
The plane - a Cessna 206 - was carrying seven people on a route between Araracuara, in Amazonas province, and San Jose del Guaviare, a city in Guaviare province, when it issued a Mayday alert due to engine failure in the early hours of May 1.
Three adults, including the pilot, died as a result of the crash and their bodies were found inside the plane.
Preliminary information from the civil aviation authority, which coordinated the rescue efforts, suggests the children escaped the plane and set off into the rainforest to find help.
Rescuers, supported by search dogs, had previously found discarded fruit the children ate to survive, as well as improvised shelters made with jungle vegetation.
Airplanes and helicopters from both Colombia's army and air force participated in the rescue operations.
Reuters