No accurate figures are available yet about the number of people the ferry was carrying when the accident happened, reports Xinhua news agency.
"With pain and sadness, we follow up the ferry incident in the city of Mosul, which killed dozens of innocent women, men and children," Abdul Mahdi said in a statement issued by his office.
The Iraqi prime minister "extends his condolences to the families of the victims and the people of Iraq," the statement said.
He has ordered "an immediate investigation into the incident (to be carried out) within 24 hours to show the truth and to bring those who are behind the incident to justice," it added.
Earlier in the day, a civil defence source said dozens of people, mostly children and women, drowned in the Tigris River when a ferry, owned by a tourism office, was carrying passengers from the bank of the river to a tourist island in the river in northern Mosul.
The ferry was overloaded with more than 100 people, the source said, adding that the ferry was originally designed to carry some 30 people.
--IANS vc