The news came one day after Pentagon's plan of repositioning roughly 1,000 US troops withdrawing from northeastern Syria into western Iraq, while leaving some forces at At Tanf garrison in southern Syria.
USA special forces were withdrawn from northern Syria amid growing chaos after Turkey began military operation in the region earlier this month.
The South Carolina Republican has expressed outrage in recent weeks following Trump's decision to pull USA forces out of Syria and abandon their Kurdish allies amid an onslaught from Turkey. "And we never gave the Kurds a commitment that we'd stay for the next 400 years and protect them", he said.
Esper did not specify where exactly troops would be stationed in western Iraq, and said he would soon be discussing with allies what the "next phase of counter-ISIS campaign" will look like.
"We believe we can reach an agreement with them to work together in the future, just like we have before", Cavusoglu said. Several hundred will remain in southern Syria at the Al-Tanf outpost.
Acting chief of staff Mick Mulvaney told "Fox News Sunday" that "the quickest way to get them out of danger was to get them into Iraq".
When asked about Trump's claims that the troops were coming home, Esper told reporters, "Well, they will eventually".
The United States now has 5,200 troops posted in Iraq, deployed as part of a Washington-led coalition against the Islamic State group.
Trump hinted over the weekend about the plan by tweeting that USA troops had "secured the Oil".
He said the sudden withdrawal of United States troops could take "weeks not days", and said the president has approved keeping some forces in At Tanf in southern Syria, which has served as a strategic base for training Syrian opposition groups and countering ISIS threats. The U.S. had pulled out in 2011 when combat operations ended there, but went back in three years later when Islamic State took over large parts of the country before later losing what it had gained.
Speaking to CNBC's Wilfred Frost in a taped interview that aired on Closing Bell, Pompeo said, "we prefer peace to war".
The additional U.S. troops would add to the more than 5,000 American troops already based in the country, training Iraqi forces and helping to ensure that Islamic State militants do not resurge. "We see a stability of the lines, if you will, on the ground".
American forces have permission from the Kurdish regional government to transit through Iraq but have no approval to stay there, a statement said today. "The US withdrawal continues apace from north-eastern Syria. we're talking weeks, not days", he added. They also said more than 80 Kurdish militants had been captured alive or had surrendered to Turkish forces.
Turkey says it wants to return Syrian refugees to the areas evacuated.
The Pentagon is now considering keeping a small US force in north-eastern Syria to protect oilfields.