However, Trump's sudden announcement in December that he would withdraw USA forces from Syria alarmed allies and many current and former US officials, who worry that Islamic State militants remain a threat.
Trump has loudly and repeatedly offered fawning praise for Kim, claiming that they "fell in love" and have "fantastic chemistry".
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. "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.
Mr Saleh said on Monday that the USA had not asked Iraq's permission to do so.
"I want to be able to watch Iran", he added, but denied he had plans to strike Iraq's neighbour.
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Iraqi President Barham Salih told a forum in Baghdad on Monday that the US president had not asked for permission to use its base for such purposes. "The US is a major power ... but do not pursue your own policy priorities, we live here".
President Trump announced in December that the military would withdraw from Syria, but according to the Defense Department, approximately 2,000 ISIS fighters remained where US forced had previously been operating.
He also stressed that "it is of fundamental interest for Iraq to have good relations with Iran" and other immediate neighbours.
Former Iraq Prime Minister Haider Al-Abadi chimed in as well, writing on Twitter: "Iraqi sovereignty must be respected". Iraq should not be used as a spring board to attack its neighbors.
"I am not under pressure to be out by a specific date", he said, but "the fact is, the president made a decision and we are going to execute his orders here to withdraw forces from Syria and, as we do that, we're going to do that in a very deliberate manner".
"They're starting to, as we gain the remainder, the final remainder of the caliphate of the area, they'll be going to our base in Iraq, and ultimately some will be coming home", Trump said when asked when the troops in Syria would be returning.