Tony Blair has spoken to the family of a British man taken hostage in Iraq, said Downing Street.
Ken Bigley's kidnappers say they want Iraqi women prisoners freed
It is thought he said there were "limitations" to what the government could do to secure Ken Bigley's release, said the BBC's Norman Smith.
Mr Bigley's son had urged Mr Blair to help save his father's life, following the murder of a US captive.
Earlier on Tuesday Foreign Secretary Jack Straw also sought to reassure the family of the 62-year-old engineer.
Mr Straw is thought to have said the government could not bow to the demands of the captors for Iraqi women prisoners' release.
But he wanted to reassure the family British officials in Baghdad were working to help Mr Bigley, said the BBC's Jonathan Beale.
Political correspondent Norman Smith said it was understood the prime minister spoke to several members of Mr Bigley's family at their home in Liverpool.
He told them he appreciated no one could comprehend the agony they must be going through, said our correspondent.
A website thought to be linked to the group holding the British man and two Americans - the Tawhid and Jihad group - features a video showing one of the other men being beheaded.
The group, loyal to suspected al-Qaeda leader Abu Musab al-Zarqawi, has threatened to kill another of their captives in the next 24 hours unless their demands are met.
On BBC News 24 Mr Bigley's son Craig had urged Mr Blair to "meet the demands... two women for two men".
BBC political editor Andrew Marr said there was very little the UK government could do to resolve the situation.
"They can make appeals..but they can't negotiate and they won't negotiate," he insisted.
He said Mr Blair would not want to say anything that would either provoke the group, nor appear to suggest he was prepared to enter into serious negotiations.
"He can't move either way, there's almost nothing he can say at the moment," Marr added.
A nine-minute long video tape released by Tawhid and Jihad - which has not been verified - showed five militants dressed in black behind the sobbing man, blindfolded and wearing an orange jumpsuit.
After reading a statement, the man in the centre, believed to be Mr Zarqawi himself, appeared to pull what looked like a knife and cut the man's throat.
The group has demanded the release of women it says are held by coalition authorities in the Abu Ghraib and Umm Qasr prisons in Iraq.
But the US has said no women are held at either jail, although two female "security prisoners" are held elsewhere.
They include Dr Rihab Rashid Taha, a senior scientist who worked on Saddam Hussein's bacterial weapons programme and was nicknamed Doctor Germ.
Following the broadcast of the killing, the US recovered a body which it named as Eugene Armstrong.
Mr Bigley, who is from Liverpool, Mr Armstrong and Jack Hensley, were kidnapped from the garden of their home in the Mansour district of Baghdad on Thursday.
They had been working for Middle East-based general services and construction contractor Gulf Supplies and Commercial Services.
Craig Bigley, 33, said: "I ask Tony Blair personally to consider the amount of bloodshed already suffered."
Gary Teeley, a Briton who was held hostage in Nasiriyah, southern Iraq, for six days in April, told BBC Radio 4's Today programme he had feared for his life at every moment.
"All you are depending on is answers forthcoming to questions that you ask your captors - and unfortunately the majority of the time the answer is just 'Inshallah', which means God willing," he said.
Mr Teeley said he had discovered it was thanks to two local sheikhs in Nasiriyah, and his employer, that his release was negotiated.
Earlier Mr Blair said Britain would "stand firm" against terrorists.
Iraqi interim Prime Minister Iyad Allawi, attending talks in London, said his government would "not negotiate with hostage-takers and... terrorists".
More than 100 foreigners have been abducted by insurgents in Iraq over the past 17 months.