"I need you to help me Mr. Blair because you are the only person now on God's earth that I can speak to. Please, please help me see my wife who cannot, cannot go on without me. She really can't," Bigley says in the video.
The 62-year old British engineer asks Blair to show some of the compassion that "you say you have" and accept the hostage takers' demands. Those demands are to release Iraqi women held in coalition-run prisons.
But the British government today ruled out meeting the hostage takers' demands.
British Foreign Secretary Jack Straw said that bargaining with terrorists would only assure more people would be kidnapped in the future.
"I'm afraid to say [that Bigley's video plea] can't alter the position of the British government and, as I've explained to the family, we can't get into a situation of bargaining with terrorists because this would put many more peoples' lives at risk, not only in Iraq, but around the world," Straw said.
Bigley's plight has stirred strong emotions in Britain. If he is killed, he will be the first Briton to die at the hands of hostage takers, who already have killed some 30 foreigners.
Britain's largest-selling daily, "The Sun," ran as its headline today: "Ken's Plea: Save Me Tony."
The paper wrote in an accompanying commentary that "Ken Bigley's cowardly captors got him to beg for his life in a calculated bid to turn public opinion against the [Prime Minister]. They may well succeed." Britain's participation in the U.S.-led coalition in Iraq remains unpopular with many Britons.
Other British newspapers called on the British government to refuse to deal with the hostage takers even as they expressed sympathy for Bigley's family.
An editorial in "The Daily Telegraph" said that "it is not easy for the Prime Minister to tell the country that he is powerless to save the life of a British hostage. That, alas, is the case ? To do so would be a betrayal of every other Westerner in Iraq and throughout the Muslim world."
As the British government takes a firm no-bargaining position with Bigley's captors, there were initially mixed signals from the Iraqi government over how it would respond to the crisis.
National security adviser and State Minister Qassim Dawud said yesterday that one of two prominent Iraqi women detainees might be released conditionally by judges for lack of evidence. But he said the release of Rihab Taha -- who is accused of working on weapons-of-mass-destruction programs under Saddam Hussein -- would not occur for some time and is not related to the hostage takers' demands.
However, interim Prime Minister Iyad Allawi said today that the government is not willing to allow Taha's release. Taha is being held by U.S. forces along with Huda Ammash, a woman who also accused of working on former banned weapons programs.
Coalition officials say that apart from a few such prominent figures, they are holding no Iraqi women in U.S. or British-run prisons in Iraq.
Like Britain, Italy is also in the midst of a highly emotional drama over the kidnapping of two of its citizens.
An Iraqi militant group has announced on an Islamist website that it put to death female aid workers Simona Pari and Simona Torretta of Italy, who were seized along with two Iraqi colleagues from their office in central Baghdad on 7 September.
The group, which called itself the Jihad Organization, said it had killed the women because Italy had not obeyed its call to withdraw its forces from Iraq.
However, the speaker of Italy's lower house of parliament, Pierferdinando Casini, said today that the government was treating the claims of execution "with total suspicion" because they were "unreliable."
The seizure of the two aid workers has riveted the Italian public, which already has seen two Italians killed by kidnappers in Iraq. Security guard Fabrizio Quattrocchi was killed in April and journalist Enzo Baldoni in August.
Ordinary Italians interviewed in Rome by Reuters today expressed disbelief that two women who had gone to Iraq to conduct aid programs for children could be murdered by extremists.
Businessman Luca Ghini put his feelings this way: "I don't think two girls who were there to do what they were doing should suffer a fate like that...I'm reading the newspaper now, but who knows what's really happening?"
Like London, the Italian government has refused to negotiate with the hostage takers.
But during the past two weeks of captivity for the two Italian women, Rome has launched an intensive diplomatic effort to enlist regional leaders in pressing for their release.
Italian Foreign Minister Franco Frattini made an extensive tour of the Gulf countries this month but gave no immediate word of whether he had achieved any breakthroughs.
Meanwhile, two French journalists also remain in captivity since they were kidnapped south of Baghdad in August. The French government immediately launched a high-level diplomatic effort to win the hostages' release, but their fate remains unclear.
[For additional news, background, and analysis on events in Iraq, click here.]