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Iraq is a country we’ve had a very direct relationship with, very direct investment and engagement with, not to mention the lives of our soldiers who were lost there, providing this opportunity to them,” Mr. Kerry told reporters at the end of a conference in London on combating sexual violence in conflict zones. “And I don’t think anybody in the region, or in this administration, believes it is in the interest of the United States to turn our backs on that.”

The spread of ISIL violence, meanwhile, has triggered fears of a return of the sectarian civil war between Sunni and Shiite Muslims that tore through Iraq during the middle years of the U.S. occupation.

Moktada al-Sadr, the influential Shiite Iraqi cleric whose followers were accused of some of the most horrific atrocities inflicted on Sunnis during the 2006-2007 war, called Wednesday for the creation of a special forces outfit to defend religious sites in Iraq.

His calls were followed Friday by an even more senior Shiite cleric in Iraq. In a rare intervention, the ayatollah said in a message at Friday prayers in the holy Iraqi city of Karbala that people should unite to fight back against ISIL, the Daily Star Newspaper in Beirut said.

The comments came a day after the president and foreign minister of Shiite-dominated Iran, which shares a long border with Iraq to the east and north, both vowed to help the government of Iraq’s Shiite Prime Minister Nouri al-Maliki in the fight against ISIL.

On Friday, Iranian security officials said the Islamic Republic had begun deploying Revolutionary Guard units to Iraq, The Wall Street Journal reported.

The Obama administration appeared to be caught off guard by the Iranian comment about intervening on Thursday.

Asked whether the administration would support an incursion of Iranian troops into Iraq, State Department spokeswoman Jen Psaki told reporters: “I don’t have any analysis from our team at this point in terms of what specific constructive role they could play.”

“These comments and these reports are new,” Ms. Psaki said.

Pressed more broadly on whether she believed the U.S. and Iran could forge a common approach toward supporting the government of Iraq’s Shiite prime minister, Ms. Psaki said she was “just not going to get ahead of where things stand right now.”

“I think the fact is we’ve been out there, obviously, long supporting the Iraqi government,” Ms. Psaki said. “You know where the Iranians stand.”

On Friday, Pentagon Press Secretary Rear Adm. John Kirby also appeared to have limited information on Iran’s presence inside Iraq. “I don’t have anything to confirm Iranian special forces in Iraq,” he said.

Pushed on what role Iran should play amid the increasingly unstable scenario, Adm. Kirby added: “I’m not going to write an action plan for the [Iranian] government to play in the region.”

Maggie Ybarra contributed to this report.