Iraq’s president has hit back at comments made by Donald Trump, saying that the US president did not ask Iraq’s permission for US troops stationed there to “watch Iran”.

A day after Trump said US soldiers in Iraq would be tasked with monitoring Iran, Barham Salih told reporters at a forum in Baghdad that the US military presence in the country was the result of a bilateral agreement with the specific goal of fighting terrorism.

“Don’t overburden Iraq with your own issues,” Salih said on Monday. “The US is a major power ... but do not pursue your own policy priorities, we live here.”

It was of “fundamental interest” for Iraq to have good relations with Iran and other neighbouring countries, Salih added.

Combating Iranian influence in the region has emerged as the cornerstone of the Trump administration’s Middle East policy. The US decision to reimpose sanctions lifted under former president Barack Obama, as well as new measures targeting Iran’s oil, banking and shipping industries has left Baghdad caught in the middle of growing tensions between its two biggest allies.

In an interview with CBS aired on Sunday evening Trump said Iraq was “perfectly situated for looking at all over different parts of the troubled Middle East rather than pulling up,” adding that Iran was a “real problem”.

“We’re going to keep watching and we’re going to keep seeing and if there’s trouble,” he said. “If somebody is looking to do nuclear weapons or other things, we’re going to know it before they do.”

The fortune the US spent on the Ayn al-Assad airbase west of Ramadi must be used effectively and US troops must stay in the region to protect Israel, the president continued.

Hassan Karim al-Kaabi, Iraq’s deputy speaker of parliament, said Trump’s latest comments were a “blatant and overt violation of sovereignty and national will”, according to local media.

Trump also angered Iraqi politicians in December after a three-hour visit to troops at Ayn al-Assad over Christmas, which did not include meetings with the Iraqi prime minister, Adel Abdul-Mahdi, or any other officials.

The US is reportedly in negotiations with Baghdad over redeploying some of the 2,000 special forces currently stationed in north-east Syria to American bases in Iraq, following Trump’s surprise decision last December to withdraw from the country.

US troops in Kurdish-held Syria – deployed in the fight against Isis – have also acted as a buffer between US-allied Kurdish militias and neighbouring Turkey – which has threatened a full-scale military offensive to dismantle Kurdish groups it says are a terrorist threat.

Many analysts believe the decision will serve to strengthen Iran’s presence in Syria, allowing Tehran greater access to oilfields in the north-east and unchecked freedom of movement for Iranian-backed forces in the border region with Iraq.