The former Archbishop of Canterbury has condemned the beheading of US hostage Nick Berg in Iraq as "barbaric".
Mr Berg's family knew he had been beheaded before news of the video
He also warned that the "shameful abuse of Iraqi prisoners" had indicted the West in the eyes of the Arab world.
"It's cruel, it's horrible... it can so easily lead into direct violence as that decapitation has done," Lord Carey told BBC Radio 4's Today programme.
The Foreign Office described pictures of the murder, shown on an Arabic-language website, as "indefensible".
The Bush administration has vowed to catch the killers of Mr Berg who filmed themselves cutting off his head after seizing him in Iraq.
His captors said they were avenging the abuse of Iraqi prisoners, new images of which are to be released on Wednesday.
The British Red Cross said it was "shocked and appalled" by the footage.
Lord Carey, who sparked criticism recently by saying not enough Islamic figures had condemned suicide bombers, said he feared recent events had created a "climate of paranoia" on both sides that could be a precurser to "a real clash, and that worries me".
"The decapitation of that American - that's quite awful, barbaric, it needs to be condemned," he told Today.
Lord Carey: Abuse of Iraqi prisoners is 'shameful'
"I want to gain here Muslim leaders around the world who I know repudiate that kind of action, but it's fuelled by hostility, by abuse of Iraqi prisoners.
"We have got to go deeper, we've got to confront one another, but we have got to build deeper and stronger links of dialogue and friendship."
Lord Carey, who stepped down as archbishop in 2002, told Today: "I use the word barbaric of the decapitation - I want to use the word shameful of the abuse of Iraqi prisoners.
"It's deeply shameful and it indicts us all in the West. It's cruel, it's horrible and it's degrading and those images I think feed that deep paranoia.
"It can so easily lead into direct violence as that decapitation has done.
"It's not going to help at all. I don't know how we can pull out of this. Apologies are not enough.
"Somehow it goes back to the deep hatred of one another that we have of the Muslim world and they have of us."
Lord Carey said there was "no doubt" that Britain's involvement in the Iraq war had "deepened a sense of hostility among Muslim people in our country and around the world".
He said while he believed the government had taken "justifiable action" in removing Saddam Hussein, who he described as "an evil man", he regretted that it had been without greater UN support.
Lord Carey insisted Britain had a "moral responsibility" to give money and aid to Iraq and to help rebuild that country.
But he added: "We have got to support our troops and we have got to pull out as quickly as possible."
Lord Carey conceded that religion was part of the problem, but he said differences between beliefs could be transcended.
The CIA is checking claims that top al-Qaeda suspect Abu Musab al-Zarqawi was involved in the killing of Mr Berg.
The poor-quality video of the murder was preceded by a caption announcing that al-Zarqawi would carry out the killing.
The BBC's Justin Webb, in Washington, says the murder has produced a rare moment of political unity amid the increasingly partisan divisions over the abuse of Iraqi prisoners by US soldiers.
But Nick Berg's distraught family have partly blamed the US-led coalition for creating the circumstances in which he was abducted, about a month ago.