Iraq's President Barham Saleh has rebuked Donald Trump over his comments that he wanted to maintain a US military presence there to watch Iran.
Mr Trump told CBS on Sunday he intended to keep an "incredible" base being used by US troops to combat the jihadist group Islamic State "because I want to be looking a little bit at Iran".
Mr Saleh said on Monday that the US had not asked Iraq's permission to do so.
It should stick to fighting terrorism and not pursue other agendas, he added.
There are an estimated 5,000 US military personnel in Iraq authorised to train, advise and assist Iraqi security forces in their fight against IS, which has not fully controlled any territory in the country for more than a year.
In the CBS interview Mr Trump defended his recent decision to withdraw the 2,000 US troops deployed in neighbouring Syria to support a Kurdish-led militia alliance seeking to capture the last pocket of IS territory there.
He said the troops would soon be moving to the huge Al Asad Airbase in Iraq's Anbar province and that their new tasks would include protecting Israel and keeping an eye on Iran, which his administration has accused of being the world's leading state sponsor of terrorism and of wanting to acquire nuclear weapons.
"We spent a fortune on building this incredible base. We might as well keep it," he said. "And one of the reasons I want to keep it is because I want to be looking a little bit at Iran because Iran is a real problem."
When asked if the troops stationed in Iraq could be used to strike Iran, Mr Trump responded: "All I want to do is be able to watch."
He added: "If there's trouble, if somebody is looking to do nuclear weapons or other things, we're going to know it before they do."
However, the remarks caused a stir in Iraq, which is a close ally of Iran.
"Don't overburden Iraq with your own issues," President Saleh told a forum in Baghdad on Monday. "The US is a major power... but do not pursue your own policy priorities. We live here."
Mr Saleh noted that under 2008 US-Iraq Strategic Framework Agreement, Washington had agreed not to use Iraq "as a launching or transit point for attacks against other countries".
He added: "Any action taken outside this framework is unacceptable."
The BBC's Paul Adams says this poses a problem for the government in Baghdad and could complicate delicate negotiations over US use of the Al Asad Airbase.
Those negotiations, he adds, have been based on the premise that Al Asad would be used to continue the fight against IS. It is something Mr Trump referred to when he visited the base in December.
But our correspondent says the US president's latest references to Iran and the need to protect Israel point to a very different set of priorities, which is causing unease in Baghdad.
Iraqi politicians allied to Iran or the influential Shia cleric Moqtada Sadr, a long-time adversary of the US who also opposes Iranian influence in Iraq, have for weeks been calling on the government to remove of all foreign troops from the country.