Abadi rejects Iran-backed militia's demand for Trump ban retaliation
Both Iran and Iraq are included in Trump's order to ban people from seven Muslim-majority countries from travelling to the US.
Iraq's leader Haider al-Abadi faced calls last week to respond in kind to the ban, just like Tehran did the day before.
But the prime minister warned the Shia leaders that a ban on Americans would jeopardise US support for the war on the Islamic State group currently raging in Iraq's second city of Mosul.
While the Shia leaders agreed that the US order was unfair, it was understood that Iran's allies had no alternative plan on how to finish the battle in Mosul without US help.
Abadi said at a news conference on Tuesday that Iraq was best served by preserving the US alliance. "We are ... in a battle and we don't want to harm the national interest," he said.
Iran's allies are, nevertheless, preparing to press their cause again should relations deteriorate further between Washington and Iran after Mosul, Ahmed Younis, a professor of international relations at the University of Baghdad, told Reuters.
One prominent Shia member of parliament warned the situation could change if the ban was extended.
"The Americans promised to review the ban in three months," said Hassan Khalati, a lawmaker close to Sayyid Ammar al-Hakim, a prominent Shia cleric and politician who hosted Sunday's meeting.
"If it is maintained, there will be (further) pressure" on the government to retaliate, he said.
Iran's dominant influence in Iraqi politics was eroded after IS routed the Iraqi army, commanded then by Prime Minister Nuri al-Maliki, who was a close ally of Tehran. This forced Maliki to seek US help to fight the IS militants.
Unlike Maliki, Abadi has kept Iran at arm's length. Iranian Major-General Qassem Soleimani, who oversaw the formation of the Popular Mobilisation militias receded from public view in mid-2015.
But several policy-makers and analysts said the travel ban was changing the dynamic, in particular by empowering the pro-Iranian factions.
"Why should we trust the new American administration?" asked Iskandar Witwit, a lawmaker from Maliki's bloc, the biggest in parliament. "We have the right to get closer to Iran as a secure ally in order to preserve our national interests.
Iraq this week asked the US ambassador to Iraq to convey a request to reconsider the ban, arguing for the need to cooperate against IS and saying no Iraqi was involved in attacks on US soil.
Among Iraqis affected by the ban are a top general spearheading elite forces in the fight against IS who's family is in the US, and a Yazidi lawmaker who will not able to accept a human rights award in America because of the restrictions.