Speaking in Saudi Arabia on Oct. 22, Secretary of State Rex Tillerson said "Any foreign fighters in Iraq need to go home." (Reuters)

Secretary of State Rex Tillerson on Sunday urged Iranian-backed militias in Iraq to “go home,” and warned European companies doing business with the Revolutionary Guard in Iran that they could face “great risk” from sanctions.

Shiite militias mostly composed of Iraqi citizens but backed by Iran were instrumental in helping the Iraqi army drive the Islamic State from Mosul and other strongholds in Iraq. There have been reports of Iranian advisers among them. Tillerson said they have no business being on the battlefield now that the Islamic State has been routed.

“Certainly, Iranian militias that are in Iraq, now that the fight against Daesh and ISIS is coming to a close, those militias need to go home,” Tillerson said at a news conference with Saudi Foreign Minister Adel al-Jubeir, using two common acronyms for the Islamic State. “Any foreign fighters in Iraq need to go home, and allow the Iraqi people to rebuild their lives with the help of their neighbors.”

A senior U.S. official indicated that Tillerson was referring to the Iranian-backed popular mobilization units and the Quds Force of the Revolutionary Guard Corps.

“The position of the Iraqi government and the position of our government is that there should be a single Iraqi security force answerable to the Iraqi state,” said the official, speaking on the condition of anonymity to a pool reporter in Riyadh, Saudi Arabia. The ideal, he added, is that the militia fighters either “go home or they integrate into the Iraqi security forces.”

Iran’s broad and growing influence in the region dominated Tillerson’s public comments Sunday, though he covered a wide variety of issues in his talks with Saudi officials. He hailed the budding new relationship between Riyadh and Baghdad, saying it could pave the way for a stronger, independent Iraq.

“We do seek to support, as does the kingdom of Saudi Arabia, a whole of Iraq, that is secure and stable and has the ability to stand on its own,” he said. “We believe this will in some ways counter some of the unproductive influences of Iran inside Iraq.”

The United States had pressed Saudi Arabia and its partners in the Persian Gulf for years after the 2003 invasion of Iraq to reestablish ties with Baghdad. Riyadh refused, saying that the situation in post-invasion Baghdad was too dangerous to locate an embassy there and that it did not want to support the Shiite-dominated government of Prime Minister Nouri al-Maliki. In recent years, under Maliki’s Shiite successor, Haider al-Abadi, the Saudis and other Arab states have tried to make up for what Jubeir on Sunday called “lost ground.”

In other remarks designed to send a message to Tehran, Tillerson also advised European companies to avoid investing in businesses linked to the Revolutionary Guard Corps, which is involved in many parts of Iran’s economy.

“Those who conduct business with the Iranian Revolutionary Guards, or any of their entities, European companies or other companies around the globe, really do so at great risk,” Tillerson said.

The threat of more sanctions is one of the most potent weapons for undercutting Iran and the 2015 nuclear deal. The potential for Iran to rejoin the world economy and improve its fortunes was the main reason Tehran agreed to limit its nuclear program in the landmark agreement with six world powers, including the United States. But the Trump administration is taking a more aggressive stance toward a country it considers a malign actor in the region, largely because of actions not addressed in the nuclear deal.

In Riyadh, Tillerson attended the inauguration of the Saudi-Iraqi Coordination Council. Abadi called the council an “important step toward enhancing relations.”

“We are facing in our region serious challenges in the form of extremism, terrorism, as well as attempts to destabilize our countries,” said Saudi King Salman. “These attempts require our full attention.”

Tillerson praised other small milestones in the improving relations, such as the August opening of a border crossing and direct flights between Riyadh and Baghdad. He said the new council can boost cooperation in the fight against the Islamic State and help with the rebuilding of infrastructure in areas liberated from the militants.

“Your growing relationship between the kingdom and Iraq is vital to bolstering our collective security and prosperity, and we take great interest in it, “ Tillerson said before the agreement establishing the council was signed.

Tillerson also talked with Saudi officials about the ongoing war in Yemen, where Saudi-led airstrikes have killed thousands of people over the past three years. The vast majority have been civilians.

Tillerson is trying to revive hopes of ending an economic embargo that four Arab countries have imposed on Qatar since June. Saudi Arabia, the United Arab Emirates, Bahrain and Egypt contend that Qatar finances terrorism, interferes in their domestic affairs and is too friendly with Iran. Doha denies the allegations and has accused Saudi Arabia of violating Qatari sovereignty and attempting to engineer a change of power.

“The dispute has had negative consequences, economically and militarily, for those involved,” Tillerson told reporters in Doha after meeting with Qatari officials. “And certainly the United States has felt the effects of that as well.”

“None of us can afford to let this dispute linger,” he added, calling on all parties to minimize the inflammatory rhetoric.

His wish went unfulfilled. Only minutes later, Qatari Foreign Minister Mohammed bin Abdulrahman al-Thani, while standing beside Tillerson at a news conference, spoke of the “so-called diplomats” from the blockading countries. “We do not see them make any diplomatic or mature statements,” he said.

Last month, after publicly showing sympathy for Saudi Arabia’s stance, President Trump offered to mediate the dispute, predicting that “you’d have a deal worked out very quickly.” But with the prolonged squabble at a stalemate, Tillerson has chided the Saudi-led bloc of countries, saying they are unwilling to sit down and negotiate as Qatar has offered to do. Tillerson has expressed pessimism at the likelihood of an imminent breakthrough.

Karen DeYoung contributed to this report.