The United States has some 2,500 troops in Iraq and 900 in Syria as part of the international coalition against the Islamic State group.
They have been engaged in months of talks with Baghdad on a withdrawal of forces, but fell short of announcing any timeline so far.
On Sunday, Iraqi Defence Minister Thabet al-Abbassi told pan-Arab television channel Al-Hadath that the coalition would pull out from bases in Baghdad and other parts of federal Iraq by September 2025 and from the autonomous northern Kurdistan region by September 2026.
The pullout is "two-phased" and "maybe we will sign the agreement within the next few days", Abbassi said.
He added that US Secretary of Defense Lloyd Austin had said in a meeting that "two years were not enough" to carry out the withdrawal.
"We refused his proposal regarding an (extra) third year," Abbassi said.
Coalition forces have been targeted dozens of times with drones and rocket fire in both Iraq and Syria, as violence related to the Israel-Hamas war in Gaza since early October has drawn in Iran-backed armed groups across the Middle East.
US forces have carried out multiple retaliatory strikes against these groups in both countries.
The Islamic State group seized parts of Iraq and Syria in 2014, and was defeated by Baghdad three years later and in Syria in 2019.
But jihadist fighters continue to operate in remote desert areas although they no longer control any territory.
Iraqi security forces say they are capable of tackling IS remnants unassisted, as the group poses no significant threat.
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