The video which has been posted on an Islamic website shows separate clips of the blindfolded diplomats.
It also shows the hostages stating their names and personal details.
The Organisation of al-Qaeda in the Land of Two Rivers has threatened to kill the two men.
The group previously claimed responsibility for the kidnapping and execution of Egypt’s envoy to Baghdad.
In Algeria, relatives of one of the diplomats made a tearful appeal for their release.
The kidnappers’ threat came as an early draft of Iraq’s much anticipated new constitution was published.
The document has been released less than three weeks before the August 15 deadline for its approval.
It lays out the framework for a new Iraq following the toppling of former President Saddam Hussein.
Islam looks set to play a large part in shaping the constitution.
The draft declares “Islam is the official religion of the state.”
“No law that contradicts the universally agreed tenets of Islam may be enacted.”
But the draft is still under discussion.
Parliament is due to vote on a final draft next month after which it is expected to go to a national referendum in October.
Meanwhile, the violence continued unabated after masked gunmen killed 12 Iraqi water plant workers.
A surviror said the gunmen ambushed their convoy of buses opening fire with automatic weapons, crying out “Allahu Akbar” or God is great.
Another survivor alleged that US soldiers in armoured vehicles on a nearby bridge failed to intervene.
In other violence, police said two Iraqi security personnel were killed and three wounded by mortar fire near Baiji while guarding an oil pipeline.
While six Iraqi soldiers were killed in three separate attacks in Samarra, Kirkuk and Baquba.