Okoth-Obbo will be in Syria until Tuesday, then travels to Lebanon through Wednesday, and then Jordan on Thursday and Friday. He will meet government officials and aid workers in each country.
UNHCR estimates Syria hosts about 1 million Iraqis and Jordan hosts about 750,000. Lebanon has an estimated 40,000 Iraqis.
The statement said: "Missions will be focussed on the ongoing effort to ensure that Iraqis fleeing their homeland receive international protection, that the required systems are in place ... and that there are programmes for the provision of assistance and solutions, including resettlement of the most vulnerable."