Trump, who imposed sanctions on Iran last year after pulling the United States out of the 2015 nuclear agreement, mentioned the future plans for U.S. troops in Iraq in an interview that aired before the Super Bowl.
"All I want to do is watch [Iran]. We have an unbelievable and expensive military base built in Iraq," he said. "It's perfectly situation for looking all over different parts of the troubled Middle East rather than pulling up."
Salih said Monday he wants to have good relations with its neighboring countries.
"The Iraqi constitution rejects the use of Iraq as a base for hitting or attacking a neighboring country," the Baghdad leader said. "Don't overburden Iraq with your own issues. The U.S. is a major power ... but we do not pursue your own policy priorities. We live here."
In the interview, Trump also said he thinks sending troops to Iraq in 2003 was "one of the greatest mistakes" the United States has ever made.
Trump touched on other issues in the wide-ranging interview, like reports Secretary of State Mike Pompeo might be looking to run for the Senate from Kansas.
"I asked him the question the other day, he says he's absolutely not leaving," Trump said.
The president also said he won't rule out another government shutdown or a national emergency if congressional Democrats refuse to negotiate on building a wall between the United States and Mexico.
"With Caravans marching through Mexico and toward our Country, Republicans must be prepared to do whatever is necessary for STRONG Border Security," Trump tweeted Monday. "Dems do nothing. If there is no Wall, there is no Security. Human Trafficking, Drugs and Criminals of all dimensions -- KEEP OUT!"
"I don't like to take things off the table. It's that alternative. It's national emergency, it's other things," he told CBS. "We're going to have a strong border. And the only way you can have a strong border is you need a physical barrier."
Several U.S. government agencies will shut down again on Feb. 15 if Trump and Congress don't pass a new spending bill. The last closure went on for 35 days, the longest in U.S. history. Trump has said he wants $5.7 billion to help pay for the southern border.
A national emergency would bypass Congress, but could end up facing legal challenges.
The president's remarks came two days before his postponed State of the Union address, set for Tuesday night. The annual speech is expected to touch on immigration, along with other issues like the cost of prescription drugs, Venezuela and a second summit with North Korean leader Kim Jong Un.
Trump also said military intervention in Venezuela is "an option."