Iraq is asking the U.N. Security Council to demand Turkey immediately and unconditionally pull its troops out of northern Iraq.
"This is considered a flagrant violation of the principles of the U.N. Charter and a violation of Iraqi territorial integrity and sovereignty of the state of Iraq," Baghdad's leaders wrote in a letter to the council and seen by the Reuters news agency.
Iraqi Prime Minister Haider al-Abadi already appealed to the Security Council during a televised speech earlier Friday. He said Iraq has tried to solve the dispute with Turkey peacefully and diplomatically.
"We gave our neighbor Turkey a time limit to withdraw its troops and not to close the door to dialogue," the prime minister said.
Turkish forces are in northern Iraq as part of a program to train Iraqi and Kurdish forces in fighting Islamic State.
The Turks sent in additional troops last week, however, and President Recep Tayyip Erdogan is refusing to budge. He said the additional soldiers are needed to protect the trainers from Islamic State terrorists, who he says are "running wild."
"Are we to wait for the invitation of the central Iraqi government when there is an attack to our country? We have no such luxury," Erdogan said.
Iraq says it gave no authorization for the Turkish troops to cross the border.