Major Gerardo Zamudio, a spokesman for the Philippine air force, said: "We have received reports from our tactical operations group in Davao that they have found debris near one village."
The aircraft was bound for the central city of Iloilo to pick up members of the Philippine president's security team and return them to Manila when it went missing.
The weather was reported clear at the time of the incident.
Search and rescue teams backed by military helicopters were despatched to cover a 30km radius of the airport.
Joel Parojinog, a Davao police investigator, said residents from a coastal village reported recovering two combat boots, human body parts, and some documents, including a C-130 manual.
But there is yet to be confirmation on whether the debris is from the 41-year-old Lockheed Martin aircraft which lost contact with air traffic control minutes after take-off.
The air force said it has not discounted the possibility that the C-130 was attacked or sabotaged by separatist groups battling government troops on the island.
Central and western parts of Mindanao have been the scene of intense fighting between government troops and the Moro Islamic Liberation Front (MILF) in recent weeks.
Zamudio, an air force spokesman, said the incident could affect the unit's ability to transport troops and equipment.
He added that three of the unit's five transport planes were grounded for maintenance.
Lieutenant-General Pedrito Cadungog, the Philippine air force chief, said witnesses reported hearing a loud explosion shortly after the aircraft took off.
He said he found the incident "very puzzling" because it was highly unusual for such a large aircraft to disappear without leaving any trace.
Cadungog said there were no reports of maintenance problems with the C-130, adding that US forces have been asked to help in the search.