The Pentagon had said an unsigned draft version of the letter had been mistakenly sent, but the Iraqi premier disputed that claim.
In a cabinet meeting televised on Tuesday evening, Abdel Mahdi said he had received signed and translated copies at 8:00pm local time (1700 GMT) on Monday.
The letter discussed "redeploying with an aim to withdraw from the country. The expressions were very clear," he said.
The Iraqi prime minister said preliminary versions received in Arabic and English included a translation mistake, so his office requested a correction from the US military and new versions were duly sent.
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"It was an official letter written in such a manner," Abdel Mahdi told ministers.
"It's not a piece of paper that fell off the printer or reached us by coincidence," he said.
AFP received a copy of the letter late Monday and verified its authenticity with both US and Iraqi officials.
In it, the head of Task Force-Iraq US Brigadier General William Seely informed his Iraqi counterparts that American troops were preparing to leave Iraq.
Seely wrote the US-led coalition would "be re positioning forces in the coming days and weeks to prepare for onward movement."
"In order to conduct this task, Coalition Forces are required to take certain measures to ensure that the movement out of Iraq is conducted in a safe and efficient manner," said the letter.
It said helicopters would be travelling in and around Baghdad's Green Zone where the US embassy is located as part of the preparations.
AFP could hear helicopters flying low over Baghdad throughout the night on Monday as well as Tuesday.
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