Referring to the rape and murder of a 14-year-old Iraqi girl, Abeer Qassim al-Janabi, by American soldiers last year, it said: "You should remember what you have done to our sister Abeer in the same area."
The three soldiers were reported missing after their patrol was ambushed near the town of Mahmudiya, south of Baghdad, on Saturday.
Neither al-Qaeda nor the Islamic State of Iraq have offered any evidence that they have captured the soldiers or that they are still alive.
US hunt continues
The US military has said it believed that the soldiers had been captured by fighters linked to al-Qaeda but said that the search for the men would continue.
"At this time, we believe they were abducted by terrorists belonging to al-Qaeda or an affiliated group," Major-General William Caldwell, the chief US military spokesman in Iraq, said in a statement.
"This assessment is based on highly credible intelligence information."
Caldwell said that a manhunt involving 4,000 US troops backed by jets, helicopters, sniffer dogs and spy satellites would continue until the three are found.
"I cannot promise you that these efforts will produce the results we all are praying for," he said.
"But what I can promise you the American people, and particularly the families of these missing men, is that we are doing everything we can to find these brave and courageous soldiers."
The Danish military said on Monday that one of its soldiers had died after his vehicle was struck by a roadside bomb in southern Iraq.
|Danish troops are mainly based near Iraq's southern city of Basra [AFP]|
Five other soldiers and an Iraqi interpreter were also wounded in the attack the army said.
The soldier was the seventh Danish serviceman to die in Iraq.
Denmark has about 470 troops in Iraq, mainly stationed near the southern city of Basra.
Anders Fogh Rasmussen, the Danish prime minister, announced in February that he would withdraw the troops in August.
They are to be replaced by a unit of four helicopters and 50 men, who will work alongside the British until December.