Iran calls that "psychological warfare", and a British commander cast doubt on US military concerns about threats to its roughly 5,000 soldiers in Iraq, who have been helping Iraqi security forces fight Islamic State jihadists.
The US State Department said employees at both the US embassy in Baghdad and its consulate in Erbil, capital of the semi-autonomous Kurdistan region, were being pulled out immediately due to safety concerns.
It was unclear how many personnel were affected, and there was no word on any specific threat. Visa services were suspended at the heavily-fortified US missions.
"Ensuring the safety of US government personnel and citizens is our highest priority ... and we want to reduce the risk of harm," a State Department spokesman said.
Also on Wednesday, Germany, which has 160 soldiers in Iraq, and the Netherlands which has 169 military and civilian personnel, suspended military training operations, citing increasing regional tensions.
The Dutch embassy in Baghdad said on its Twitter account that it remained open. The French army had no plans to suspend military training activities in Iraq, a source close to the defence ministry said.
"DANGEROUS SITUATION"
Both the United States and Iran have said they do not want war, and Iraqi Prime Minister Adel Abdul Mahdi said on Tuesday he had indications "things will end well" despite the rhetoric.
Iraq is one of the only countries that has close relations with both the United States and Iran. It has said it will keep strong ties with Iran, and also with both the United States and regional Arab neighbours, some of whom, such as Saudi Arabia, consider Tehran an arch-rival.
The United States, which occupied Iraq from 2003-2011 after invading to topple dictator Saddam Hussein, sent troops back there in 2014 to help fight Islamic State. Iran has close ties to powerful Iraqi political parties and supports powerful Shi'ite militia groups.