The ruling given late on Saturday denied a request from the US Department of Justice to immediately restore Trump's order, which a judge in Washington state had blocked on Friday.
"It is a move in the right direction to solve the problems that it caused," the Iraqi spokesman, Saad al-Hadithi, told Reuters.
Trump's executive order last week put a 120-day halt on the US refugee program, barred Syrian refugees indefinitely and imposed a 90-day suspension on people from seven majority Muslim countries - Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.
Religious minorities persecuted by the Islamic State group, and other Iraqis fleeing violence, were among those affected.
The ban would have prevented a total of 20,000 people in "precarious circumstances" in the seven countries targeted from resettling in the US during the 120 days covered by the suspension, according to the United Nations.
Baghdad protested against the ban, calling it unfair and saying that no Iraqi had been involved in attacks on US soil.
But it refrained from retaliating as it seeks to maintain US support for Iraqi forces battling Islamic State in Mosul.
The US has more than 5,000 troops deployed in Iraq, providing critical air and ground support for Iraqi and Kurdish forces fighting the militants, who declared a self-styled caliphate over parts of Syria and Iraq in 2014.
,It is a move in the right direction to solve the problems that it caused,, said Saad al-Hadithi, Iraqi spokesman.
Iraq is satisfied with a US appeals court ruling against a travel ban imposed by US President Donald Trump, a government spokesman said on Sunday.
