On Wednesday, Italian aid agency Intersos told Aljazeera.net that it will not be stopping operations in Baghdad.
Secretary-General Nino Sergi said: "We have no intention to leave Iraq now. We will continue operations and this is the position shared by other Italian non-governmental organisations including A Bridge for Baghdad."
Dr Sergi spoke after armed men abducted four aid workers, including Mahnaz Bassam, an Iraqi Intersos staff member.
On Tuesday two Italian women, Simona Torretta and Simona Pari, who worked for the Italian charity Un Ponte Per Baghdad (A Bridge to Baghdad), were kidnapped.
Two of their Iraqi colleagues were also kidnapped in broad daylight from their offices in a residential neighbourhood of the capital.
Erwin van Land, spokesman for Medecins Sans Frontieres, told Aljazeera.net: "We have obviously discussed security measures for our staff in Iraq, but our decision remains to stay.
Police guard a building where the
four aid workers were kidnapped
"Our work will continue in Baghdad, including work in our three clinics in Sadr City. We have 90 staff in Iraq, and most of them are Iraqi although we do have a small number of international staff."
Several other non-governmental organisations (NGOs) that did not want their names to be disclosed for security reasons, backed these claims, stating no decision had been made to leave Baghdad.
Initial reports surfaced after Jean-Dominique Bunel, an official from an agency that coordinates the activities of aid workers in Iraq, said on Wednesday NGOs were leaving the country.
"It seems that most foreign NGOs are preparing to leave, and some expatriates already left this morning," Bunel said.
"The others should do the same thing in days to come," he added.
"The reason they are leaving is that this is a new modus operandi: the kidnappers entered their office right in the middle of Baghdad and women are being taken hostage," Bunel said.
According to the Frenchman, there are some 50 NGOs in Iraq that count at least one foreigner among their staff.