The acting defence secretary, who flew in from Afghanistan on his foreign tour since taking office last month, is due to hold talks with Prime Ministrer Adel Abdel Mahdi and top military advisers and commanders.
Trump's comments about Iran, in an interview with CBS television aired on February 3, drew a stern rebuff from President Barham Saleh, who said the use of Iraq as a base against a third country violated its constitution.
They also sparked renewed calls for a US withdrawal both from pro-Iran factions within the government and from Iran-trained armed groups whose power has risen sharply during the fightback against the Islamic State group that culminated in December 2017.
But with US-backed Kurdish-led fighters poised to overrun the Islamic State group's last tiny enclave in eastern Syria, perhaps as early as this week, the withdrawal, which other administration figures had managed to slow, is now likely to gather pace.
Trump's comments about the Al-Assad airbase came after the US president had already angered Iraqi leaders in December by paying a Christmas visit to US troops based there without travelling to Baghdad to talk with them.
"We spent a fortune on building this incredible base. We might as well keep it," Trump said in the CBS interview.
At a rare joint news conference on Monday, the two groupings demanded at the very least a "new agreement" setting tight conditions on any future foreign troop presence.
Following the US-led invasion that overthrew since-executed dictator Saddam Hussein in 2003, US troop numbers peaked at some 170,000 before a full withdrawal was completed in 2011.
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