President Donald Trump signed the order midday in the Oval Office, according to the White House. A previous version of the travel ban, which was mired in legal challenges, was revoked.
The pressure from the Iraq officials included a phone call between Trump and Iraqi Prime Minister Haider al-Abadi on February 10 and an in-person conversation between Abadi and Vice President Mike Pence in Munich on February 18.
Those conversations were followed by discussions between Secretary of State Rex Tillerson and members of the Iraqi government about vetting measures in place that would prevent suspected terrorists from leaving Iraq and coming to the United States.
Tillerson described his efforts in public remarks Monday after the new order had been signed.
"Iraq is an important ally in the fight to defeat ISIS, with their brave soldiers fighting in close coordination with America's men and women in uniform," he said. "This intense review over the past month identified multiple security measures that the State Department and the government of Iraq will be implementing to achieve our shared objective of preventing those with criminal or terroristic intent from reaching the United States."
Tillerson thanked Abadi for his "positive engagement and support for implementing these actions."
Officials in Baghdad welcomed Iraq's removal from the list of countries affected by the travel ban.
"(The) Iraqi Foreign Ministry expresses deep relief regarding the executive order that was issued by the American President Donald Trump, which excludes the Iraqis from the travel ban to the United States," said foreign ministry spokesman Ahmad Jamal.
"This is considered an important step in the right direction that strengthens and reinforces the strategic alliance between Baghdad and Washington in many fields, in particular the fight against terrorism," Jamal added.
In Trump's call with Abadi, the President vowed to seek a resolution to his counterpart's concerns about his citizens being unable to enter the United States, according to a readout of the phone call from Baghdad. The US official said Trump asked Tillerson to get greater clarity on vetting measures in Iraq.
Trump also faced pressure to remove Iraq from the order from some American national security officials, who argued the restriction burdened a key anti-ISIS partner. Some of those voices were holdovers from the Obama administration.