Lord Carey said they were facing systematic ethnic cleansing which had worsened considerably since the fall of Saddam Hussein.
The mainly Christian community has faced relentless persecution for hundreds of years from the largely Muslim population living alongside them.
Lord Carey today joined members of the Assyrian community in London at the House of Lords to launch a campaign raising awareness of their plight. He said: “In recent months and years churches and monasteries have been attacked and people have been killed.
“In one case a young man was kidnapped and beheaded. We are talking about terrible atrocities which would undermine any community.
“It is systematic violence against Assyrian people, driving them out of their homes and pillaging them.
“It is putting pressure upon them to get them to leave.”
The ancient civilisation, which has existed since 3,000 BC, has one of the oldest Christian traditions in the world, dating back to the first century.
About 800,000 Assyrians live in Iraq with an additional half a million around the world. They still speak the ancient biblical language of Aramaic.
Prof Simo Parpola, an expert on Assyrian culture, told the meeting that the current violence was on a par with the massacres during the First World War when 250,000 were killed.
Mark Seddon, campaign organiser, said: “There does appear to be a degree of ethnic cleansing going on now.”
He called for Assyrian rights to be enshrined in the new Iraqi constitution and for Assyrians dispossessed by the violence to be given the financial aid to return to their lands and homes.
The Rev Doctor Khoshaba George, who runs an Assyrian church in London, said hopes had been raised with the fall of Saddam in 2003.
But he added: “We were waiting more than 40 years for the change of regime and hoping for a bright and new future for Iraq and our nation.
“Unfortunately things went wrong and our condition in Iraq is becoming worse and worse.”
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