Title: Iraqi Interim Government
Content:  It was recognized by the U.S., the United Nations, the Arab League and several other countries as being the sovereign government of Iraq (see Iraqi sovereignty for more information). The U.S. retained significant de facto power in the country and critics contend that the government existed only at the pleasure of the United States and other coalition countries, whose military forces still remain in Iraq. The coalition did promise that its troops would leave if the new sovereign government requested it, but no such request was made.
Title: Caretaker government
Content:  Iraq is governed by a caretaker government.
Title: Iraq
Content:  The federal government of Iraq is defined under the current Constitution as a democratic, federal parliamentary republic. The federal government is composed of the executive, legislative, and judicial branches, as well as numerous independent commissions. Aside from the federal government, there are regions (made of one or more governorates), governorates, and districts within Iraq with jurisdiction over various matters as defined by law. The National Alliance is the main Shia parliamentary bloc, and was established as a result of a merger of Prime Minister Nouri Maliki's State of Law Coalition and the Iraqi National Alliance. The Iraqi National Movement is led by Iyad Allawi, a secular Shia widely supported by Sunnis. The party has a more consistent 
Title: Government of the Islamic Republic of Iran
Content:  The Government of the Islamic Republic of Iran (, known simply as Neẓām among its supporters) is the ruling state and current political system in Iran, in power since the Islamic revolution and fall of the Pahlavi dynasty in 1979. Its constitution, adopted by an ex post facto referendum, uses separation of powers model with Executive, Legislative, and Judicial systems, while the Supreme Leader is the country's head of state and commander-in-chief of the armed forces. It is currently one of the three governments using the title Islamic republic.
Title: Foreign involvement in the Syrian civil war
Content:  The Iraqi Government has sent Assad financial support since 2011. Iraq has opened its airspace for use by Iranian planes ferrying support to the Syrian government, and has granted passage through Iraqi territory to trucks bound for Syria carrying supplies from the Iranian Revolutionary Guards. The Iraqi government has signed a deal to provide Syria with diesel fuel. Iraq has struck ISIL in Deir ez-Zor several times. In December 2018, the Syrian government officially gave Iraq the green light to strike ISIL inside Syrian territory without first asking permission.
Title: Islamic republic
Content:  with Islam as a state religion and that are (at least partly) ruled by Islamic laws, but do not carry the "Islamic republic" name - examples include Iraq, Yemen, Algeria and Maldives. Iran officially uses it as a title in all governance names referring to the country (e.g. the Islamic Republic of Iran Army or the Islamic Republic of Iran Broadcasting) as opposed to its equivalents in Pakistan which are called the Pakistan Armed Forces and the Pakistan Broadcasting Corporation. Unlike the others, Iran also uses the IRI acronym of the Islamic Republic of Iran as part of official acronyms.
Title: Federal government of Iraq
Content:  The federal government of Iraq is defined under the current Constitution, approved in 2005, as an Islamic, democratic, federal parliamentary republic. The federal government is composed of the executive, legislative, and judicial branches, as well as numerous independent commissions.
Title: Politics of Iraq
Content:  The politics of Iraq take place in a framework of a federal parliamentary representative democratic republic. It is a multi-party system whereby the executive power is exercised by the Prime Minister of the Council of Ministers as the head of government, as well as the President of Iraq, and legislative power is vested in the Council of Representatives. The current Prime Minister of Iraq is Mustafa Al-Kadhimi, who holds most of the executive authority and appointed the Council of Ministers, which acts as a cabinet and/or government.
Title: Iran–United States relations after 1979
Content:  Iran has taken an active role in Iraq. Talks between the two nations (Iran and Iraq) have been successful, with Iran even going so far as to build a major Iranian Bank branch inside Iraq. Iran stresses that it supports the government of Iraq. Indeed, the main party that supports the Iraqi government and the US coalition, SCIRI, is also close to Iran. Its leader, Abdul Aziz al-Hakim, who has been invited at the White House, was a refugee in Iran when Saddam Hussein was the leader of Iraq. On 21 February 2007, his own son, coming from Iran with armed guards, was arrested by US forces and later released with excuses by US forces. The US have, 
Title: Iran–Iraq War
Content:  The relationship between these two nations has warmed immensely since the downfall of Saddam Hussein, but mostly out of pragmatic interest. Iran and Iraq share many common interests, as they share a common enemy in the Islamic State. Significant military assistance has been provided by Iran to Iraq and this has bought them a large amount of political influence in Iraq's newly elected Shia government. Iraq is also heavily dependent on the more stable and developed Iran for its energy needs, so a peaceful customer is likely a high priority for Iran, foreign policy wise.  The Iran–Iraq War is regarded as being a 

Question: what government does iraq use?
Answer: Prime Minister of Iraq.