Foreign nationals are being urged to flee Iraq as governments and private companies react to growing insecurity and a wave of kidnappings.
Seven Chinese were freed - but other foreigners are still being held
Coalition civilian spokesman Dan Senor said on Tuesday that 40 hostages from 12 countries were being held in Iraq.
A French journalist taken hostage on Sunday has been freed by his captors.
Russia has announced that it will be evacuating all of its citizens and other ex-Soviet nationals by air at the end of the week.
France has followed Germany in issuing a formal warning urging its citizens to leave, calling the kidnappings "unacceptable".
The British Foreign Office said it continued to advise against all but the most essential travel to Iraq.
A number of other foreigners have been taken hostage or reported missing in Iraq including three Japanese citizens abducted last Thursday whose fate remains unknown.
CONFIRMED FOREIGN HOSTAGES
1 Israeli Arab
Their captors threatened to burn them alive unless Japan withdrew its 550 troops from Iraq - but the 11 April deadline passed without any news of their fate.
Japan's defence chief Shigeru Ishiba has given up a plan to visit the country's troops in southern Iraq, due to security concerns, reports quoting official sources said.
Four Italian employees of a private US securoity agency have also been abducted.
Three Czech television journalists were also taken hostage north of Baghdad on Monday morning.
Mr Senor said: "We are making it clear that there will be no negotiations with hostage-takers and... that it is everyone's interest that these hostages be released as expeditiously as possible."
Other hostages have been released. Three Russian and five Ukrainian engineers abducted by insurgents in Baghdad were freed unharmed on Tuesday, one day after they were kidnapped.
And seven Chinese men seized near the flashpoint town of Falluja on Sunday were also released after being held for a day.