Jeanine Hennis-Plasschaert, the Special Representative of the UN Secretary-General for Iraq and Head of the United Nations Assistance Mission for Iraq (UNAMI), met with the Secretary-General of the Asa'ib Ahl al-Haq movement, Qais Al-Khazali, on Tuesday.
Khazali has its own armed group, which is part of the Iraqi Popular Mobilization Forces (PMF). He is seen as closely aligned with Iran and was involved in past attacks on US troops in Iraq.
Hennis-Plasschaert previously met him last November to discuss the results of October's parliamentary elections.
"They discussed the current political situation in the country, including the formation of the new government," UNAMI tweeted on Wednesday.
So far, Turkey has denied responsibility for the attack.
The attack was discussed on Tuesday at the UN Security Council in New York.
Earlier on Monday, the Coordination Framework, an alliance of Shia political parties, announced they had chosen Mohammed Shia al-Sudani, a former Iraqi human rights minister and member of the State of Law, as their candidate for prime minister.
Khazali claimed that the selection came without "foreign interference."
Sudani's candidacy for the position of prime minister was previously rejected in 2019, Iraq expert Joel Wing wrote on his blog.
The leader of the Sadrist movement, Muqtada al-Sadr, who failed to form a "national majority government", previously opposed his candidacy.
"Sudani will have an uphill battle to become the next premier and if he does gain the position he could face protests organized by Sadr who wants to be kingmaker despite withdrawing his followers from parliament," Wing wrote.
In an earlier statement this week, Khazali also called on the Kurdistan Democratic Party (KDP) and Patriotic Union of Kurdistan (PUK) to choose an Iraqi presidential candidate.
Without a presidential candidate, it will be difficult to form a new government.
So far, both Kurdish sides have not agreed on a single candidate.
The KDP's candidate is Reber Ahmed, the current Kurdistan Region's Interior Minister, while the PUK's candidate is incumbent Iraqi President Barham Salih.
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