The militants added that the hostage was still alive, but had been moved to the place where he was to be killed.
The group that snatched truck driver Angelo dela Cruz, 46, near restive Fallujah initially gave the Philippines until 11 p.m. Sunday Baghdad time to agree to pull its troops out of Iraq by July 20.
The Philippine government previously rejected that ultimatum.
Meanwhile, insurgents killed three U.S. soldiers and an Iraqi civilian in separate attacks.
Also, Iraqi interim president Ghazi al-Yawer said his government will soon offer an amnesty to those who have fought against the U.S.-led coalition, a British newspaper reported Monday.
"We are offering an amnesty definitely, for people who have not committed too many atrocious acts," al-Yawer was quoted as telling The Financial Times. "Everybody except murderers, rapists and kidnappers."
He said the amnesty would be offered within "a couple of days."
In other recent developments:
According to a video and a statement read on the pan-Arab television station Al-Jazeera, Angelo dela Cruz's kidnappers said they were extending the deadline for 24 hours, until Monday night.
On the video, dela Cruz pleaded with the Philippine president, Gloria Macapagal Arroyo, to withdraw the troops before they were scheduled to leave Aug. 20 so that he wouldn't be killed.
However, he also asked that his body be delivered to his country.
The militant group, the Iraqi Islamic Army-Khaled bin Al-Waleed Corps, said it had done everything in its power to prove it had wanted to spare his life.
In the video, dela Cruz appeared to wearing an orange garment similar to those worn by two other hostages who have slain: American Nicholas Berg and South Korean Kim Sun-il.
A militant deadline for two other hostages — Bulgarian truck drivers held by a separate group demanding the release of all Iraqi detainees — expired Saturday morning. The militants had threatened to execute the Bulgarians if the U.S. military did not release all Iraqi detainees by the deadline.
On Sunday, Bulgarian Foreign Minister Solomon Pasi said he had unconfirmed information the hostages were still alive.
Pasi appealed to the hostage takers, saying Islam calls for "mercy for the poor, the hungry and the sick." He said one hostage, Georgi Lazov, had diabetes, while the other, Ivaylo Kepov, had suffered a stroke.
The group holding the Bulgarians — the Tawhid and Jihad movement linked to Jordanian terror suspect Abu Musab al-Zarqawi — also claimed responsibility for Thursday's attack on a military headquarters in Samarra that killed five U.S. soldiers and an Iraqi National Guardsman.
To prevent the infiltration of foreign fighters, Syria and Iraq agreed to create a special force to patrol their 360-mile shared border, Iraqi Deputy Prime Minister Barham Saleh said Sunday in Damascus, Syria, after meeting with Syrian President Bashar Assad.