The sprawling new consulate, one of the biggest U.S. diplomatic missions in the world, is in the Masif area about eight miles from Erbil, which is also home to Kurdish leader Massoud Barzani and other senior officials from his party. Iraqi political parties including Mr. Barzani’s party and a bloc loyal to the Shiite cleric Moqtada Sadr are in the process of trying to form a government after elections last year resulted in heavy losses by traditional Iranian-backed parties.Mr. Sadr, whose coalition is the biggest single bloc in the Iraqi Parliament, and who has had a tumultuous relationship with Iran over the years, condemned the strike. On Twitter, he described the attack as an attempt to sow division, saying the Kurds were “the lung of Iraq and a part of a whole that cannot be divided.”Iraqi President Barham Salih, who is Kurdish, said the timing of the attack was aimed at obstructing the process of government formation. “We must stand firmly against attempts to plunge the country into chaos,” he said in a statement.Since the U.S.-led invasion of Iraq in 2003, Iran has expanded its security, political and religious influence in the country by funding and training militia groups, some of them with political wings. Over the years, those fighters have battled American troops, Sunni insurgents and the militants of the Islamic State.Iran has said that its goal is to drive the U.S. military out of Iraq entirely, even in its current role of providing advice and assistance to Iraq’s military without engaging in combat. In the past few years, many Iraqis have pushed back against Iran’s influence, seeing it as foreign meddling destabilizing their country.Shortly after the attack Sunday, social media and Telegram accounts affiliated with the Islamic Revolutionary Guards Corps posted videos that showed missiles setting off a massive fireball and a giant plume of smoke. Tasnim News Agency, which is affiliated with the Revolutionary Guards, said that in addition to the dozen missiles, 14 BM-21 Grad rockets also struck targets in Erbil.