"We urge the abductors to release the hostages immediately. Nothing can justify this criminal act," Xinhua quoted Rasmussen as saying.
During his visit to Ankara Monday, Rasmussen will meet both President Abdullah Gul and Prime Minister Recep Tayyip Erdogan regarding the hostage issue, the ministry said.
On Wednesday, a group of armed militants of the Islamic State in Iraq and Levant (ISIL) took control of the Turkish consulate in Mosul in Iraq and kidnapped 49 Turkish citizens, including diplomats, soldiers and children.
ISIL has also taken 31 Turkish nationals as hostages from a power plant in the Gyarah region of Mosul.
On Tuesday and Wednesday, ISIL seized Mosul and Tikrit, another provincial capital, in its renewed clashes with the Iraqi government forces.
Besides the hostage issue, Rasmussen's will also discuss about the preparations for the run-up to the NATO's upcoming summit in Wales in September.