Decades-old arch enemies the United States and Iran have vied for influence in Iraq since the 2003 US-led invasion toppled dictator Saddam Hussein.

Both helped Iraq to defeat the Islamic State group, and the United States still has 2,500 non-combat troops in the country to provide it with advice and training.

Some 900 US troops remain in Syria, most in the Kurdish-administered northeast, as part of a US-led coalition battling remnants of IS.

And the US Navy's Fifth Fleet is based in Bahrain, across the Gulf from Iran.

"Americans are not friends with anyone and are not even loyal to their European friends," Ayatollah Ali Khamenei said at his meeting with Iraq's President Abdul Latif Rashid, the supreme leader's website said.

"Even the presence of one American in Iraq is too much."

Earlier, Rashid met President Ebrahim Raisi and held a joint news conference.

"We do not consider the presence of foreign forces and foreigners in the region to be useful," Raisi told reporters.

"The presence of the US disturbs the security of the region," said the Iranian president.

"Our relationship with Iraq is based on common interests," he said, adding the "Americans think about their interests, not the interests of the countries in the region".

Although Iraq and Iran fought an eight-year war in the 1980s, relations between the Shiite-majority neighbours have warmed considerably since the 2003 invasion ousted Saddam and his Sunni-dominated regime.

Iraq has become a key economic lifeline for the sanctions-hit Islamic republic, while Iran provides Iraq with gas and electricity as well as consumer goods.

At the news conference with Rashid, Raisi stressed the importance of Iran's cooperation with Iraq in security and other matters.

"Relations between Iran and Iraq will continue in the field of water and electricity infrastructure," he said.

"A security understanding has been established between the two countries, and the security of Iraq and its borders is very important to us," Raisi added.