BAGHDAD — US forces that crossed into Iraq as part of a pull-out from Syria do not have permission to stay and can only be there in transit, the Iraqi military said on Tuesday.

US Defense Secretary Mark Esper said, however, that Washington aimed eventually to bring the troops withdrawing from Syria back to the United States.

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 Daesh (the so-called) militants and "to help defend Iraq".

"All US forces that withdrew from Syria received approval to enter the Kurdistan Region so that they may be transported outside Iraq. There is no permission granted for these forces to stay inside Iraq," the Iraqi military said.

Esper said Washington's objective was for the troops not to remain in Iraq.

"The aim isn't to stay in Iraq interminably, the aim is to pull our soldiers out and eventually get them back home," Esper said at the Prince Sultan Air Base near Riyadh, Saudi Arabia.

Esper said the details had not yet been worked out on how long the US troops would stay in Iraq and he would be having discussions with his Iraqi counterpart on Wednesday.

It is unclear whether the US troops will use Iraq as a base to launch ground raids into Syria and carry out air strikes against Daesh militants.

The additional US troops would add to the more than 5,000 American troops already based in the country, training Iraqi forces and helping to ensure that Daesh militants do not make a comeback.