While the State Department did not explain its reasons, such shifts in staffing generally indicate Washington sees a lower risk of conflict.

"Personnel who are temporarily located outside of Iraq will begin a gradual return to the US embassy in Baghdad and consulate" in the northern Kurdish city of Arbil, State Department spokeswoman Tammy Bruce told reporters.

She said the State Department still advised Americans not to travel to Iraq.

Iran's clerical government has wide influence over armed Shiite groups in Iraq who have at times targeted US forces.

The United States on June 22 ordered staff out of Iraq as President Donald Trump ordered strikes on Iranian nuclear sites as part of a military campaign by Israel.

Iran responded by firing missiles at a major US base in Qatar but Trump said that Iran had telegraphed its intentions, giving time to shoot down the projectiles. Soon afterward Trump declared a ceasefire between Israel and Iran.

The easing of travel restrictions comes despite a series of drone strikes on oil fields in the Kurdistan region.

There were no claims for the strikes, which came amid a dispute between Kurdish authorities and the central government on oil revenue, which headed toward resolution on Thursday.

Bruce condemned the attacks, saying they "imperil Iraq's stability and economic future."

"The government of Iraq has a duty to protect its territory and all of its citizens," she said.

The State Department on June 22 also ordered out family members and non-emergency employees from Lebanon, where Iran holds sway over Shiite movement Hezbollah, but lifted the order on July 3.