WASHINGTON (Reuters) - US forces pulling out of Syria have not been given permission to stay in Iraq, the Iraqi security media cell said on Monday, amid US Defense Secretary Mark Esper's assertion that Washington is ultimately aiming to bring troops back from Syria to the United States, contradicting previous Pentagon expectations.

The cell added that the forces that arrived in the Kurdistan region of Iraq two days before coming from Syrian territory entered with the consent of the Baghdad government in order to facilitate the transfer process outside Iraq, stressing in a statement that the Iraqi approval required the transfer of these forces outside Iraqi territory.

In turn, Iraqi military sources indicated that these forces have already left Iraqi territory towards Kuwait.

Esper said Washington's goal was not to keep US troops in Iraq. "The aim is not to stay in Iraq for a long time. The goal is to withdraw our soldiers and bring them home eventually," he said in remarks at Prince Sultan Air Base near Riyadh, Saudi Arabia.

He said details of the time US troops would spend in Iraq had not been discussed and he would hold discussions with his Iraqi counterpart on Wednesday.

Contradiction and ambiguity
The Iraqi army statement contradicts the Pentagon's announcement that almost all 1,000 US troops withdrawn from northern Syria are expected to move to western Iraq to continue the campaign against IS and "support the defense of Iraq."

"All US forces have withdrawn from Syria and have been granted permission to enter the Kurdistan region to be transferred out of Iraq. There is no consent to remain within Iraq," the Iraqi army said in a statement.

It is not yet clear whether US forces will make Iraq a base for ground attacks in Syria or air strikes on IS fighters.

Before US troops crossed from Syria, more than 5,000 US troops were stationed in Iraq to train Iraqi forces and help ensure that ISIS did not rise again.