Thamer al-Sabhan is the first Baghdad-based Saudi ambassador in a quarter century, but while full diplomatic relations are restored, many Iraqi Shiites view Riyadh as a supporter of jihadist groups and an enemy of their community.
Sabhan said in interview with Al-Sumaria television that the Hashed al-Shaabi paramilitary forces, which are dominated by Iran-backed Shiite militias, are not wanted in Sunni Arab and Kurdish areas as "they are not accepted by the sons of Iraqi society".
While they have been a key part of the anti-IS fight and are widely supported by Iraqi Shiites, many members of the Sunni Arab and Kurdish minorities view at least some of the Hashed al-Shaabi's main forces as hostile.
"The remarks of the Saudi ambassador indicate clear hostility and blatant interference in Iraqi affairs (and) his talking about the Hashed al-Shaabi in this way is considered a major insult," Khalaf Abdulsamad, the head of the Dawa parliamentary list, said in a statement.
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Alia Nasayif, an MP from the State of Law bloc, said the ambassador's remarks "included clear attempts to provoke sectarian strife".
And Hashed al-Shaabi spokesman Ahmed al-Assadi termed Sabhan an "ambassador of a state that supports terrorism" and called for Iraq to "expel this ambassador and punish him for his statements."
But Sabhan's comments were not universally panned, with the Alliance of Iraqi Forces, the main Sunni Arab bloc in parliament, describing his remarks as "very natural" and criticising the "political campaign" against him.
Saudi Arabia's execution of activist and Shiite cleric Nimr al-Nimr at the beginning of the month sparked widespread anti-Riyadh anger, protests and calls for Sabhan to be kicked out of Iraq.
Iraq has been plagued by years of tensions between its Shiite majority and Sunni minority, which ruled the country under Saddam Hussein, with thousands killed in sectarian violence.
The United Nations said last week that more 18,000 Iraqi civilians had been killed in the previous two years, many due to an upsurge in violence with the rise of IS.