Iraq summoned the new Saudi ambassador Sunday after he suggested Iranian-backed Shiite militias were exacerbating sectarian tensions and should leave the fight against Islamic State to the Iraqi army and official security forces.

Baghdad's move underscores the depth of enmity between Sunni and Shiite Muslim powers as sectarian conflicts rage in Syria, Yemen and Iraq. Riyadh only reopened its embassy in Baghdad last month. It had been shut down since the Iraqi invasion of Kuwait in 1990.

In an interview with Iraq's al-Sumaria TV Saturday, Saudi envoy Thamer al-Sabhan criticized the Hashid Shaabi, a coalition of mostly Iranian-backed Shiite paramilitary groups seen as a bulwark against the Islamic State Sunni militants whose rise has inflamed sectarian tensions in Shiite-majority Iraq.

"The refusal by the Kurds and (the Sunni province of) Anbar to let the Hashid Shaabi come to their regions shows that the Hashid is not accepted by Iraqi society," Sabhan said.

Iraq's foreign ministry called the remarks "a break of diplomatic protocol and based on inaccurate information".

"The Hashid Shaabi are fighting terrorism and defending the country's sovereignty and acting under the umbrella and command of the commander-in-chief of the armed forces," it said in a statement.

Earlier Iraqi Shiite lawmakers accused Sabhan of meddling in domestic affairs, including recent violence in eastern Diyala province where Sunni mosques and residents were attacked in apparent retaliation for blasts targeting Shiite militia fighters claimed by Islamic State.

"If such interference is repeated, there will be calls to declare the ambassador persona non grata and demand that the Kingdom of Saudi Arabia replace him," Khalid al-Assadi, a member of Parliament's foreign affairs panel, said by phone.

Local media published similar comments from other Shiite lawmakers.

"He should be expelled immediately or else he could meet dire consequences," Awatef Nemah from the ruling Shiite bloc told al-Sumaria, without elaborating.

The reopening of the Saudi embassy in Baghdad has been seen as heralding closer cooperation in the fight against Islamic State militants, who control swathes of territory in Iraq and Syria and have claimed bombings in Saudi Arabia.

But it has also coincided with a fresh escalation of tensions between Sunni Muslim Saudi Arabia and Shiite Iran, longtime regional rivals, after Riyadh executed a prominent Shiite cleric this month.