In a hastily arranged news conference on Monday, Esper said the United States has not made any decision to leave Iraq.
Reporters were later told the letter was actually a draft document intended only to explain the increased movement of the troops.
"We respect your sovereign decision to order our departure", the letter added.
It came in reaction to a U.S. precision drone strike on Baghdad that killed Iranian general Qassem Soleimani and top Iraqi commander Abu Mahdi al-Muhandis, among others. He now faces a tricky balancing act. PM Mahdi's statement On Tuesday Iraqi caretaker PM Adel Abdel Mahdi confirmed that he had received the draft letter described by General Milley that described steps the United States military would take to move out of Iraq. They have also been embroiled in a proxy conflict in Iraq and elsewhere in the region.
In the U.S., the Democrats were outraged that Mr Trump had failed to inform Congress in advance about the air strike against the Iranian military commander.
Adel Abdul-Mahdi, who resigned in November amid mass anti-government protests, said Iraq wants a U.S. troop withdrawal to avoid further escalation as tensions soar between American and Iran.
House Speaker Nancy Pelosi was discussing the situation in Iran when she received a note with news of the attack, said parliamentarians present at the meeting.
The Trump administration has had more than its share of fiascoes, but the letter to Iraq on the withdrawal of us troops is proving to be one of the most extraordinary. "We're not leaving unless they pay us back for it". He was addressing a gathering of Iranians who chanted "Death to America".
"The initial Iranian response to the assassination of the martyred commander Soleimani has happened".
Iraqi militia commander Abu Mahdi al-Muhandis was buried in the southern Iraqi city of Najaf earlier on Wednesday.
Lawmakers from both groups boycotted Sunday's parliament session.
One source said early indications were of no US casualties, while other USA officials declined to comment.
In a statement, Senator Payne said the resolution passed by Iraq's Parliament was non-binding, and in the meantime, the Australian Government was working through the possible implications should it be formally approved by the Iraqi Government. "The Secretary General noted that the suspension of North Atlantic Treaty Organisation training activities is a temporary force protection measure and that North Atlantic Treaty Organisation is prepared to continue its activities when the situation permits", the press release from PMO said.
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