Militants in Iraq have killed the second of two US civilians they were holding hostage, according to a statement on an Islamist website.
A video showing Mr Hensley was released shortly after the abduction
The murdered man is thought to be Jack Hensley, who was abducted from Baghdad last week with two other men.
One of them, Eugene Armstrong, was seen in a video released on Monday being killed by a masked man - thought to be al-Qaeda suspect Abu Musab al-Zarqawi.
A threat to kill Briton Kenneth Bigley, the last hostage, has been renewed.
The men were kidnapped by militants claiming to be from the Tawhid and Jihad group, headed by Mr Zarqawi, on Thursday.
On Monday, after killing the first hostage, they issued a new 24-hour deadline for the release of all women from US-run prisons in Iraq.
"The nation's zealous sons slaughtered the second American hostage... after the end of the deadline," said the statement posted on one Islamist website on Tuesday.
It added that a film of the slaughter would be provided shortly.
A statement on another website said Mr Bigley would also be killed if the group's demand was not met.
The authenticity of the statements has not been verified.
A statement about the death of the first hostage appeared on the internet on Monday shortly before the online appearance of video footage apparently showing Mr Armstrong being beheaded.
The US embassy later recovered Mr Armstrong's body.
The CIA said on Tuesday it had a high degree of confidence that Mr Zarqawi was the man who carried out the beheading.
In a meeting with Iraqi interim leader Iyad Allawi on Tuesday, US President George W Bush condemned the killing of Mr Armstrong.
"We all stand in solidarity with the [remaining] American that is now being held captive," he said.
Mr Hensley's wife Patty earlier made a fresh appeal to her husband's kidnappers.
Women in custody
The son of Mr Bigley, the British hostage, has meanwhile appealed to the UK government to give in to the militants' demands.
US authorities say they only have two women in their custody in Iraq - both of them scientists allegedly involved in former leader Saddam Hussein's weapons programme.
UK authorities have said there are no Iraqi women in jails under their control.
Tawhid and Jihad claims to have killed at least six hostages in Iraq, the first one being Nicholas Berg, a US businessman who was beheaded in May.
More than 100 foreigners have been abducted by insurgents in Iraq over the past 17 months, as part of a campaign to destabilise the US-backed interim government and drive foreign troops out of the country.
They include two French journalists who were abducted almost a month ago and two female Italian aid workers, along with two of their Iraqi colleagues, who were kidnapped on 7 September.