Mazin Abdullah, secretary-general of the IRCC, told Al Jazeera there was no evidence about the identities of the kidnappers.
Brigadier-General Abdel Karim Khalaf, chief of operations at the interior ministry, said: "We received information that a kidnapping took place in the area and we dispatched several security units to investigate."
The Iraqi Red Crescent, which is part of the International Committee of the Red Cross, is the only Iraqi aid agency working in all of the country's 18 provinces and has around 1,000 staff and 200,000 volunteers in the country.
There have been several mass abductions in Baghdad in recent months.
Men dressed in military uniforms took dozens of shop owners and bystanders from a commercial area in central Baghdad on Thursday.
|Blair, left, made a surprise visit to Baghdad |
where he met the Iraqi prime minister
Tony Blair met with Nouri al-Maliki, his Iraqi counterpart, in the fortified Green Zone in Baghdad on Sunday and vowed not to let democracy be destroyed by "those who wish to live in hatred".
Speaking at a news conference after the meeting Blair said that he and the Iraqi prime minister had discussed the need for national reconciliation and the building-up of Iraq's security forces to fight the Shia-Sunni sectarian violence that has pushed the country close to all-out civil war.
Blair pledged his support to the Iraqi government saying: "We stand ready to support you in every way that we can so that in time the Iraq government and the Iraqi people can take full responsibility for their affairs."
Asked about concerns that Syria and Iran were not doing enough to help in Iraq, Blair answered: "It's important that we exercise all the pressure and authority that we have to make sure that all countries in the region are supporting Iraq.
"There's a very strong obligation which is set out in the UN resolution for all countries in the region to be supportive of the Iraqi prime minister and his government ... and not undermine them."
Blair had arrived in Iraq after a visit to Egypt as part of a tour of the region.
US forces accused
In other news, the Iraqi Red Crescent has accused US forces of carrying out a spate of attacks on its offices over the last three years during operations to flush out suspected fighters.
Jamal Al Karbouli, vice-president of the IRC, told a news conference in Geneva on Friday: "The main difficulties we are facing, first of all, is the presence of MNF, the multinational forces, which sometimes gives us a hard time. They are attacking some offices and detaining some volunteers."
Karbouli said US forces had "attacked" its Baghdad headquarters a number of times since the invasion in 2003. In most of the incidents, the Americans claimed to have received "information."
"We don't know the reason behind it, is it to scare us or decrease our work or another reason, as they mention, fear of terrorists? We don't know."
The US military in Iraq said it was checking the allegations but said its forces do not attack sites while conducting searches.