Hosham Dawod's comments, made to the BBC, came as people marked the anniversary of the January 3, 2020 US drone strike near Baghdad's international airport that killed Soleimani and his Iraqi lieutenant, Abu Mahdi al-Muhandis.

Soleimani headed the foreign operations arm of Iran's Islamic Revolutionary Guard Corps, while Muhandis commanded the powerful, state-sponsored pro-Iranian Hashed al-Shaabi paramilitary network. The duo had worked closely together.

"Soleimani didn't think he was just a co-coordinator with Iraq," Dawod told the BBC.

"He actually believed himself responsible for Iraq. That is why he entered and left (the country) when he wanted."

Pro-Iranian supporters have accused Kadhemi of complicity in the drone strike, which last year brought Washington and Tehran to the brink of war.

"The founding principles of the Iraqi state were not in his (Soleimani's) priorities," Dawod said.

"So, with Qaani, we, the Iraqi government, made him apply for a visa," he added, referring to Soleimani's successor, Esmail Qaani.

Dawod's comments sparked an angry reaction from Ahmed al-Assadi, one of the leaders of the Hashed's parliamentary bloc, who said that Soleimani had been entering Iraq "officially and legally" and had been there to "help the government and the people".

Assadi poured scorn on Dawod, a French-Iraqi anthropologist, and praised Soleimani, noting that the Iranian military commander was on the frontlines in the fight against the Islamic State group in Iraq.

"Where was this 'advisor' when Soleimani went from trench to trench to defend Iraq, until his blood was spilt at the international airport?" Assadi asked.

Since making the comments, Dawod's post as advisor to the premier has been "frozen" on Kadhemi's orders, an Iraqi official told AFP on condition of anonymity.

Dawod issued a statement "to apologise to all those who misunderstood his words".

But other lawmakers, such as Mehdi al-Amerli, a member of the parliamentary defence committee, demanded Kadhemi sack Dawod immediately or to "clearly state his position".

Shoalan Abu al-Jon, a lawmaker from the pro-Iran Badr armed faction, said that Kadhemi "no longer deserves to remain" as leader.

"A prime minister who does not act, and does not say a word to defend the Iraqis and Iraq's guests, must resign," he said.