The statement comes after the kidnappers released a video in which the victim, Warren Rodwell, appealed to give the rebel group whatever they ask for to ensure his freedom.
Rodwell, 53, is an English teacher from Sydney and married a 27-year-old Filipino woman in June. He was taken Dec. 5 from his home in the seaside town of Ipil, the capital of Zamboanga Sibugay province, a report in The Manila Times newspaper said.
The kidnappers took Rodwell at gunpoint and are demanding $2 million to set him free.
"The Philippine government has a strict no-ransom policy and will not negotiate with terrorists," spokesman for the Western Mindanao Command, army Lt. Col. Randolph Cabangbang, said.
Around 2,000 soldiers are helping search for Rodwell, Cabangbang said.
"Our operation is continuing and we will not stop until the hostage is recovered safely," he said.
The video shows Rodwell pleading for his life.
"To the government, to the Filipino government especially the government of Zamboanga Sibugay, Rommel, I'm appealing to you please help me to coordinate with my family to raise to whatever money is being asked," he says in the video.
"To the Australian Embassy here in the Philippines, this is your constituent appealing for his life and safety. Please help facilitate to give the group the demand."
The Australian government has said it will help Philippines authorities search for Rodwell.
Last week the U.S. State Department issued an updated travel warning to U.S. citizens visiting the Philippines. There is a heightened risk of terrorist activity in the country, the warning said.
The State Department replaced a June warning about insurgent activity in the Philippines with a warning that said terrorist attacks in parts of the country, including Manila, could be indiscriminate.
Rodwell's kidnappers are believed to be the same as those who took U.S. citizen Gerfa Lunsmann, her son Kevin Eric and a Filipino nephew in Zamboanga City in July, regional army chief, Maj. Gen. Noel Coballes said.
The kidnappers freed those hostages after the family paid a large ransom.
Zamboanga Sibugay province is on the southeastern shore of Mindanao Island, the country's area with the largest Muslim population. The federal government has been fighting disruptive Mindanao region separatist rebel groups for around 30 years.
Between 120,000-150,000 people are estimated to have been killed in the struggle.
One of the largest rebel groups, the Moro Islamic Liberation Front is involved in peace talks with the government. It said it isn't responsible for Rodwell's kidnapping and would do what it could to help authorities locate him.
The most notorious of the rebel groups is Abu Sayyaf, regarded as a terrorist organization by the United States and the Philippines. It has been accused of masterminding some of the deadliest terrorist attacks in the country, including one of the worst assaults.
In February 2010, an Abu Sayyaf group killed at least 11 people, including a 1-year-old child, in an attack on a small village on Basilan Island, just off Mindanao. Up to 17 people were wounded, including four children aged 1 to 11.
The government has had some successes in tracking down Abu Sayyaf rebels. In September, government troops killed one of the group's leaders, Imram Asgari, in a clash in a village about 20 miles outside Zamboanga City.
In late December, the 52-year-old deputy mayor of a town near Ipil was killed and his wife wounded when they went to withdraw money from an ATM in a street in Ipil.
The attacker escaped on a motorcycle driven by another person, police said. No group claimed responsibility for the attack.