Speaking at a forum in Baghdad, Salih was responding to a question about Trump's comments to CBS about how he would ask troops stationed in Iraq to "watch" Iran.
US troops in Iraq are there as part of an agreement between the two countries with a specific mission of combating terrorism, Salih said, and that they should stick to that.
Trump said the United States spent a fortune on a base in Iraq. "We might as well keep it. 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," he said in excerpts from a CBS "Face the Nation" interview.
Asked if that meant he wanted to be able to strike Iran, Trump said, "No, because I want to be able to watch Iran."
"Don't overburden Iraq with your own issues," Salih said. "The US is a major power ... but do not pursue your own policy priorities, we live here."
Iraq is in a difficult position as tensions between its two biggest allies, the United States and Iran, increase.
"It is of fundamental interest for Iraq to have good relations with Iran" and other neighbouring countries, Salih said.
Speaking at a forum in Baghdad, Salih was responding to a question about Trump's comments to CBS about how he would ask troops stationed in Iraq to 'watch' Iran.