The International Committee of the Red Cross has called for the immediate release of about 20 people seized from the Red Crescent offices in Baghdad.
Armed men wearing commando-style uniforms stormed the aid agency's office on Sunday, snatching 30 people.
Reports say that six of those kidnapped, mainly elderly men, have since been released.
The Red Cross called for the others to be freed, saying the Iraqi Red Crescent provided vital help for those in need.
"They do so with devotion and with humanity," ICRC Director of Operations Pierre Krahenbuhl said in Geneva.
"They must be respected and supported, not harmed."
Wave of attacks
The hostage-taking is the latest in a wave of such kidnappings and came as UK Prime Minister Tony Blair made a surprise visit to the Iraqi capital.
Blair on surprise Iraq visit
Officials described how a large convoy of new vehicles similar to those used by the Iraqi police drew up at the Red Crescent office in Baghdad.
Men in uniforms similar to those of the Interior Ministry's special commando forces got out and entered the building, saying they had been sent to check the premises.
Once inside, they rounded up all the men at gunpoint, including employees and visitors.
Three Iraqi guards from the nearby Netherlands embassy were also seized.
The Interior Ministry has said that none of its units had been on duty in the area at the time.
Infiltrated
The kidnappings are the latest in a long series of similar operations and the second in less than a week.
On Thursday, gunmen in military uniforms kidnapped up to 70 people from a commercial area in the Sanak area of the capital. At least two dozen people were subsequently freed.
Many of the kidnappings have been blamed on Shia militias masquerading as police commando units.
But there is also a suspicion that the police are so infiltrated by the militias that they are indistinguishable from each other, says the BBC's Jim Muir in Baghdad.
Criminal gangs seeking ransoms are also involved in kidnapping.
The Iraqi Red Crescent, the country's biggest humanitarian organisation, has previously been the target of the insurgency and random attacks.
On Friday, the organisation accused US troops of attacking its office and vehicles.
The Red Crescent, which has a staff of 1,000 and 200,000 volunteers, is the only Iraqi aid group working across the country's 18 provinces.
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