A group calling itself the Khalid Ibn al-Walid Brigade has threatened to behead Filipino truck driver Angelo de la Cruz.
The captors are pressuring the Manila government to agree by Tuesday to a withdrawal of its handful of troops from Iraq within nine days - one month earlier than scheduled.
But President Gloria Arroyo has bluntly refused to succumb to the threat.
"Our government's stand remains the same as we cannot change our commitment given to the international community," a senior Philippine diplomat in Baghdad said.
Adding to the drama, which has gripped the Philippines and grabbed headlines around the world, the captive's wife and brother left the Philippines for Jordan in a last-ditch bid to secure his release.
Arsenia de la Cruz is to make a personal appeal for the freedom of her husband, a 46-year-old father of eight, who was seized last week as he drove a truckload of crude oil from neighbouring Saudi Arabia.
Iraqi authorities and the US-led military have said they are doing everything possible to resolve the crisis safely but as the clock ticks down for de la Cruz there was no new information.
stand remains the same as we cannot change
our commitment given
to the international community"
"The multinational force is deeply concerned about the well-being and safety of the individuals who are missing and presumed held hostage by anti-Iraqi forces," the US military press office said.
"We are actively pursuing and engaging multiple intelligence and other sources as to the whereabouts and circumstances of these individuals," it said.
Of dozens of foreigners captured since April, some have been released and others killed.
Meanwhile, Bulgaria's Foreign Minister Solomon Passy said two Bulgarian lorry drivers - held and threatened with execution unless US occupation troops freed Iraqi prisoners within 24 hours - were still alive despite the expiry of their execution time.
"According to unconfirmed information, our two countrymen are alive at this point," Passy said in Sofia. "We have no information about a change in the situation."
The Tawhid wa Al-Jihad group said it is holding Bulgaria's Ivailo Kepov and Georgy Lazov and also claimed responsibility on Sunday for Thursday's mortar and car bomb attack in Samarra.