In a statement, the office of President Abdul Latif Rashid said it would "summon the US embassy in Baghdad over this matter".

On Tuesday, State Department Spokesman Matthew Miller expressed concern about political attacks in Iraq against Cardinal Louis Raphael Sako.

"We are disturbed by the harassment of Cardinal Sako, the patriarch of the Chaldean church, and troubled by the news that he has left Baghdad," Miller said.

"We are concerned that the Cardinal's position as a respected leader of the church is under attack from a number of quarters."

For several months, Sako has been embroiled in a war of words with a Christian lawmaker, Rayan al-Kildani.

Kildani heads the Babylon Movement, whose armed wing is part of Hashed al-Shaabi -- a network of largely pro-Iran paramilitaries that were integrated into Iraqi security forces.

In early July, Rashid cancelled a 2013 decree officially recognising Sako as head of the Chaldean Church, and which was essential for administering the community's endowment, according to the patriarch.

In response, Sako said he has "decided to withdraw from the seat of the patriarchate in Baghdad", and would instead settle at one of the monasteries in the autonomous Kurdistan region in northern Iraq.

Miller called the treatment of Sako a "blow against religious freedom", and said Washington had made its views on the issue "quite clear" to the authorities in Baghdad.

The Iraqi presidency's statement on Wednesday said it was "disappointed by the accusations aimed at the Iraqi Government and the Presidency regarding the decision taken to reverse a decree that was not in line with the country's constitution".

It said that to reverse the 2013 decree "would be futile and a flagrant violation of the Constitution for which Iraqis and Americans themselves have fought and sacrificed".

The statement added that the president "has always respected Iraq's Christians and has advocated for their rights throughout his career".

In a country ravaged by repeated conflicts and plagued by endemic corruption, Sako and Kildani have both accused each other of illegally seizing Christian-owned properties.

Kildani, who has been under US sanctions since 2019, accuses the cardinal of assuming a political role beyond his religious mandate.

Sako, in turn, says the parliamentarian aims to gain legitimacy as the sole representative of the Christian community.

Iraq's Christian population has drastically declined since the 2003 US-led invasion that toppled strongman Saddam Hussein, dropping from more than 1.5 million people to around 400,000 today.

Many have fled the violence that has plagued the country over the past 20 years.