US President Donald Trump's surprise visit to Iraq did not include a meeting with Prime Minister Adel Abdul-Mahdi, and enraged local lawmakers, exposing rifts between Baghdad and Washington.
The two leaders instead spoke over the phone, the statement added.
After the brief visit, when Air Force One had left Iraqi airspace, Trump posted a video on his Twitter feed.
The Bina bloc, Islah's rival in parliament and led by Iran-backed militia leader Hadi al-Amiri, also objected to Trump's trip to Iraq.
"The excuse made the initial infraction all the worse", said Haddad.
But this trip came as curbing foreign influence in Iraqi affairs has become a hot-button political issue, and Trump's perceived presidential faux-pas was failing to meet with the prime minister in a break with diplomatic custom for any visiting head of state. "The American leadership was defeated in Iraq and wants to return again under any pretext, and this is what we will never allow", he said.
While there has been no full-scale violence in Iraq since Daesh suffered a series of defeats past year, some 5,200 United States troops train and advise Iraqi forces still waging a campaign against the militant group.
The president, who kept to the US air base approximately 100 kilometers (60 miles) west of Baghdad, said he had no plans to withdraw the 5,200 troops in the country.
According to a transcript released by the White House, he thanked troops for the "near-elimination" of IS and said "we'll be watching... very, very closely - the remnants" of the group.
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L'etat, c'est moi, perhaps, but in an election he will merely be one candidate among many appealing for the vote. One wild card is Benny Gantz, a popular former military chief who is flirting with the idea of entering politics.
During his visit, Obama reiterated his intention to remove to all USA troops from the country. "The United States can not continue to be the policeman of the world", he repeated to reporters, describing a long-term vision of detached isolationism embodied by his controversial decision last week to pull thousands of US troops from Syria and Afghanistan.
"Iraq is important because of its strategic location".
The US military presence in Iraq also aids "Israel's desire to block the Tehran-Beirut route" and helps offset Iran's strengthening presence in the region, he said.
"If you would have seen what we had to go through in the darkened plane with all windows closed with no light anywhere - pitch black", he said.
The US military presence was largely unwelcome for years, until Washington created the global coalition to defeat IS in 2014 and helped erase the jihadists' "caliphate". On the one hand, he still wants to demonstrate the intention to abandon the role of global policeman with the subsequent mission where American blood is spilt for the sake of a country, about which a lot of them can't find on a map. It's not entirely clear when Trump planned the visit, whether he chose to go after the decision to leave Syria on December 19, or before.
"We're no longer the suckers, folks", Mr Trump told American servicemen and women at a base in western Iraq. "I'm going to a war zone", he had said.
Fifteen years after the 2003 invasion, the USA still has more than 5000 troops in Iraq supporting the government as it continues the fight against remaining pockets of resistance by the Islamic State group.
The Iraqi response, he said, "would be the parliament´s decision to remove your military forces" unilaterally.
With Abdel Mahdi still struggling to fill key ministerial positions months after his appointment, analyst Hashemi said the "axis close to Iran will seek a parliamentary vote on a timeline for an American pullout from Iraq".