While US forces have been key to the rollback of the jihadis onslaught in Iraq in 2014, both independent and Iran-backed Iraqi political groups have been increasingly calling for ending foreign military deployment in the country.
"Don't overburden Iraq with your own issues".
In the CBS interview Mr Trump defended his recent decision to withdraw the 2,000 U.S. troops deployed in neighbouring Syria to support a Kurdish-led militia alliance seeking to capture the last pocket of IS territory there.
Salih, speaking at an global forum in Baghdad, cautioned Trump against putting his own country's foreign policy agenda over Iraq's, stating that Trump should not "pursue your own policy priorities".
He also said that some of the USA troops withdrawing from Syria will be based at al-Asad air base in western Iraq, which the president visited briefly in December.
Trump inauguration committee subpoenaed for financial documents
The head of the inaugural committee, Tom Barrack, confirmed to The Associated Press that he was questioned by Mueller in 2017. Foreigners can not contribute money to inaugural committees, political campaigns, and PACs under USA federal law.
Trump denied wanting to strike Iran, but said, "I want to be able to watch Iran. The US is a major power. but do not pursue your own policy priorities, we live here".
"It is of fundamental interest for Iraq to have good relations with Iran" and other neighbouring countries, Salih added. We've beaten them and we've beaten them badly.
Trump offered no specifics about when he would bring home the 14,000 U.S. troops now in Afghanistan.
However, the remarks caused a stir in Iraq, which is a close ally of Iran.
Officially, Iraq says there are no American bases on its soil - only instructors deployed at Iraqi bases.
But despite ISIS losing almost all of the territory it once controlled in Iraq and Syria, the Pentagon report, which was published Monday, says "despite the loss of most of its territory in Syria, DoD officials stated that ISIS continues to attract foreign fighters to Syria and Iraq", with the US-led military coalition estimating the number of foreign fighters to be "most likely 50 per month".