The two governments said the release from jungle captivity of American missionary couple Martin and Gracia Burnham was non-negotiable.
Television stations aired the Reuters footage of the Burnhams on Thursday.
The video clip showed Martin saying their captors are "targeting US, European and other Western nations" because of alleged Western indifference to persecuted Muslims and US "support" for the Philippine government’s alleged illegal occupation of Muslim lands.
National Security Adviser Roilo Golez told reporters the government will not be pressured by the showing of the Burnham footage on television.
"The government will remain steadfast in its position that there will be no conditions insofar as the (Burnhams’) release is concerned," he said. "We are not going to listen to any condition, and the US and Philippine governments are one in this position."
Golez said he had already discussed the matter with Assistant US Secretary of State James Kelley.
"He made it clear that they share our position here – no conditions and this is non-negotiable," Golez said.
He said he believed the footage shown Thursday must have been shot one or two months after the Burnhams were snatched from the Dos Palmas beach resort off Palawan in May last year.
"This can be gleaned from the physical appearance of the Burnhams because they look a lot better than how they appeared in the tapes shown (in November) where they looked very emaciated and harassed," he said.
"I cannot believe that in the past one month or so that they would be in a much healthier condition insofar as body weight is concerned because the Abu Sayyaf has been under tremendous pressure, and they have always been on the run," he added.
Wire reports said the source of the video clip claimed it was taken in mid-January this year, but the claim could not be verified.
Golez said he believed the Abu Sayyaf extremists had "pre-taped" the recent footage to "deodorize" their image because they want to introduce a political angle to their terrorist activities.
"They are trying to say that: Look, we are doing this because we are against the United States, against Israel, against so many things; to put a political motive behind the abduction," he said.
Defense Secretary Angelo Reyes said on radio yesterday that the footage must have been taken earlier than last November because the Burnhams looked healthier and more relaxed.
"We can see that they are healthier compared to the other videos that we saw," he said. "We have suspicions on who could have taken (the video), but it would be too early to divulge that. Our analysis is that, this video is intended for the foreign audience, to be shown to terrorists abroad for support."
Armed Forces spokesman Brig. Gen. Edilberto Adan also said the statement read by Martin in the video footage confirmed the military’s assessment that the Abu Sayyaf has links with the al-Qaeda terrorist network of Osama bin Laden.
"Their statement is what the al-Qaeda leaders had been saying after the Sept. 11 attack at the (World Trade Center in New York City)," he said.
On the other hand, Maj. Cynthia Teramae, spokeswoman for the US Special Operations Command, said the Abu Sayyaf cannot justify the kidnapping of innocent people.
"We stand on the belief that the (Burnhams’) return should be immediate," she said. "They are innocent individuals where they are held hostage against their will –there is no justification for that. Any rejoicing, that rejoicing will come with the release of those three individuals." – Roel Pareño, Paolo Romero, Marichu Villanueva