"All U.S. forces that withdrew from Syria have received approval to enter the Kurdistan region to be transported out of Iraq, however, there is no permission for these forces to stay," the statement read.
The Iraqi military statement contradicted the Pentagon’s announcement that all of the nearly 1,000 troops withdrawing from northern Syria are expected to move to western Iraq to continue the campaign against the Islamic State group and to help "defend" Iraq.
In addition, Secretary of Defense Mark Esper said Tuesday during his visit to Saudi Arabia that the troops will be prepared in Iraq to return to their homeland, without specifying the deadline for their return.
"The goal is not to stay in Iraq endlessly but to withdraw our soldiers and eventually bring them back home," Esper said at Prince Sultan Air Force Base near Riyadh.
Hundreds of vehicles carrying U.S. troops crossed the Syrian-Iraqi border through the Kurdish region of northern Iraq on Monday, and it is estimated that more than 5,000 troops are currently stationed in that Arab country under a bilateral agreement.
After the end of the war in 2011, the U.S. military presence in Iraq had diminished considerably, a fact that changed in 2014 with the threat of the IS.
The US military presence continues to be a sensitive and politicized issue as part of Iraqi society considers it an occupation.