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 5,000 estimated 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…