President Susilo Bambang Yudhoyono had made the request in a telephone conversation with Mrs. Arroyo, said minister, Hassan Wirayuda.
"President Arroyo said she had great concern about the issue and had ordered the Armed Forces, police and the intelligence body to take action to free the hostages," Wirayuda told reporters.
The three Indonesians Ahmad Resmiyadi, Yamin Labaso and Erikson Hutagaol were seized in March after their boat was attacked off Malaysias Sabah region by a group calling itself the Jamiat al-Islamiah of southern Mindanao.
They were now believed to be held somewhere in the southern Philippine province of Tawi-Tawi.
The Indonesian foreign minister said the captors had demanded 7.5 billion rupiah ($790,000) in ransom from the hostages employer.
Wirayuda denied last weeks media reports that one of the hostages had been executed.
"We had contact with the hostages, and they said they were being treated well," he said. "But its true that one of them contracted malaria and another had diarrhea."
Medicine had been sent to the hostages, he added.
An Indonesian envoy in the Philippines said last week that the captors had asked embassy officials to send them a camcorder so they could convey their demands on video. AFP