Iraq's parliament has passed a resolution calling for foreign troops to leave the country in the wake of a U.S. air strike that killed Iran's top military commander, Qasem Soleimani, near Baghdad last week.
Meanwhile, U.S. Secretary of State Mike Pompeo said more Iranian leaders will be targeted if Tehran retaliates.
The Iraqi government "commits to revoke its request for assistance from the international coalition fighting [the Islamic State (IS) extremist group] due to the end of military operations in Iraq and the achievement of victory," the lawmakers said in the resolution adopted on January 5.
The government of Prime Minister Adil Abdul-Mahdi "must work to end the presence of any foreign troops on Iraqi soil and prohibit them from using its land, airspace, or water for any reason," they added.
U.S. State Department spokeswoman Morgan Ortagus said the United States was disappointed in the decision.
"While we await further clarification on the legal nature and impact of today's resolution, we strongly urge Iraqi leaders to reconsider the importance of the ongoing economic and security relationship between the two countries and the continued presence of the Global Coalition to Defeat ISIS," Ortagus said in a statement, using an alternate acronym for the Islamic State group.
Pompeo has since appeared on six U.S. news shows since Soleimani was killed.
He said if Iran uses its proxy forces -- in Iraq, Syria, Yemen, Lebanon, and elsewhere -- to strike U.S. targets, a response won't be limited to them.
"They will be borne by Iran and its leadership itself," Pompeo said. "Those are important things the Iranian leadership needs to put in its calculus as it makes its next decision."
The United States has some 5,000 military personnel in Iraq, mainly as advisers.
Parliamentary resolutions are nonbinding, but Abdul-Mahdi had earlier urged parliament to take urgent measures and end the presence of foreign troops as soon as possible.
"Despite the internal and external difficulties that we might face, it remains best for Iraq on principle and practically," he told lawmakers in a speech.
Later in the day, Iraq's military said that two rockets had fallen inside Baghdad’s heavily fortified Green Zone, where the U.S. and other embassies are based, as well as the seat of Iraq's government.
Another rocket hit a nearby area, it said.
Several people were reportedly wounded in the attacks.
Soleimani, the commander of the Quds Force, the foreign arm of Iran's hard-line Islamic Revolutionary Guards Corps (IRGC), was killed on January 3 as he left Baghdad's airport in a convoy amid a regional tour.
The attack marked a significant escalation between Iran and the United States, with Tehran promising "harsh revenge."
Thousands of Iraqis attended a funeral procession for Soleimani before his body was flown to Iran, where hundreds of thousands of mourners on January 5 participated in processions honoring the commander.
In a series of January 4 tweets, President Donald Trump said he had ordered the strike on Soleimani because the Iranian commander had organized attacks on U.S. and Iraqi targets and that he was "preparing for additional hits in other locations."
"Iran is talking very boldly about targeting certain USA assets as revenge for our ridding the world of their terrorist leader who had just killed an American, & badly wounded many others, not to mention all of the people he had killed over his lifetime, including recently hundreds of Iranian protesters," Trump wrote.
"If Iran strikes any Americans, or American assets, we have targeted 52 Iranian sites (representing the 52 American hostages taken by Iran many years ago), some at a very high level & important to Iran & the Iranian culture," he also said.
Trump's reference to hostages taken by Iran refers to the takeover of the U.S. Embassy in Tehran in 1979 by Iranian revolutionaries, who held 52 Americans captive for 444 days.
The inclusion of "cultural" sites on a potential target list prompted immediate criticism from Iranian officials and observers.
Iranian Foreign Minister Mohammad Javad Zarif said the killing of Soleimani was a breach of international law and that any targeting of cultural sites would constitute a war crime.
"Those masquerading as diplomats and those who shamelessly sat to identify Iranian cultural & civilian targets should not even bother to open a law dictionary," Zarif wrote in a January 5 tweet. "Jus cogens refers to peremptory norms of international law, i.e. international red lines. That is, a big(ly) 'no no'."
Pompeo on January 5 defended the intelligence assessment that led to the air strike that killed Soleimani, saying not taking action would have posed a greater risk.
Pompeo on ABC television defended the U.S. strikes as lawful and said that any target the U.S. military may strike in Iran would be legal under the laws of armed conflict -- which prohibit the deliberate targeting of cultural sites under most circumstances.
"Every target that we strike will be a lawful target, and it will be a target designed with a singular mission -- defending and protecting America," he said.
Pompeo also said there was no doubt in his mind that Iran "gets clearly the message from the American leadership."
In remarks aired later in the day on Fox News, he said that "there is a real likelihood Iran will make a mistake and make a decision to go after some of our forces, military forces in Iraq or soldiers in northeast Syria."
Amid soaring tensions with Iran, the U.S.-led coalition battling the IS group in Iraq and Syria said on January 5 it had halted most of its operations against the militants for now to focus on protecting coalition forces and bases.
A spokesman said that the coalition could still carry out some operations and would act in self-defense against the militants.
As head of the Quds Force, the 62-year-old Soleimani helped orchestrate Tehran's overseas clandestine and military operations.
Both the force and the IRGC have been designated as terrorist organizations by the U.S. State Department.
Demonstrators took to the streets in many American cities to protest against the targeted killing by U.S. forces.
Many traditional U.S. allies have also expressed concerns that the military strike could ignite a wider conflict in the already tense Middle East, although some have defended the United States' right to defend itself.
Washington has blamed Iran for orchestrating attacks by Iraqi Shi’ite militias on U.S. and coalition sites, including an assault on the U.S. Embassy in Baghdad by a mob that included pro-Iran paramilitary groups on December 31. The attackers withdrew on January 1 and no staff was hurt.