Both the military and the president's office said they received information that the hostage was killed. The Islamic militant group Abu Sayyaf is believed to be holding more than 20 hostages in the southern Philippines.
Philippine officials were working to confirm reports on Sunday that Islamic militants beheaded a German hostage after a ransom deadline had passed.
Major General Carlito Galvez, a regional military commander, said the military received information that the 70-year-old German hostage was killed Sunday - 30 minutes after the 3 pm (0700 GMT/UTC) deadline.
"But we need proof of body," he added.
Local intelligence reports claim the beheading took place in the town of Indanan on the island of Jolo, about 1,000 km (620 miles) south of the capital, Manila.
Philippine soldiers distribute leaflets picturing an Abu Sayyaf militant with a $5million bounty on his head
Presidential Peace Adviser Jesus Dureza said that he received the same intelligence report as the military and that an anti-terrorism task force told him "validation efforts" were ongoing.
"In the meantime, the armed forces of the Philippines and other security forces are maintaining their 'search and rescue posture' until all kidnap victims are freed," he added.
The Abu Sayyaf terrorist group had demanded 30 million pesos ($600,000 or 570,000 euros) to free the German hostage who was taken from his yacht off the coast of the southern Philippines in November.
His 59-year-old wife was shot dead when she resisted the militants. Her body was later found on the boat.
Dureza said appeals were made to the captors to free the hostage, while security forces sought to rescue him ahead of the deadline.
Airstrikes against Abu Sayyaf
The military launched airstrikes Saturday against suspected hideouts of the Abu Sayyaf in a forested area in the nearby town of Patikul, where up to 60 militants were believed to have been hiding.
The army vowed it would maintain its offensive against the militants, and deployed hundreds of ground troops to carry out the offensive, according to Brigadier General Restituto Padilla, a military spokesman.
"The armed forces will pursue the enemy and dictate the terms, not the other way around," he said. "We will not be cowed by the demands of evil individuals and groups who continue to perpetuate practices contrary to Islam."
Last year, Abu Sayyaf militants beheaded two Canadian nationals after they did not receive ransom payments. The Canadians were abducted in September 2015 with a Norwegian man and a Filipino woman, who were later both freed.
The Philippine government has a no-ransom policy and discourages other parties from making payments, but not always successfully.
The Abu Sayyaf militants may be holding more than 20 other hostages in the southern Philippines. The group has been blamed for some of the worst terrorist attacks in the Philippines.
President Rodrigo Duterte has directed the military to crush the militant group and warned that it could be a source of recruitment for the so-called "Islamic State" (IS) extremist militia.
(dpa/jm (KNA, epd)