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BAGHDAD (Reuters) - Iraq’s parliament held its first session since May’s national election on Monday but failed to elect a speaker, what should have been the first step toward forming a new government.

Lawmakers were supposed to elect the speaker and two deputies, at the start of a 90-day process outlined in the constitution.

But with competing political blocs each claiming to hold a parliamentary majority, no vote was held on the appointments. The temporary leader of the assembly said it would remain in session until Tuesday.

The new cohort of Iraqi lawmakers was sworn in after a formal handover ceremony attended by the leaders of the main electoral blocs, including Prime Minister Haider al-Abadi who addressed the gathered MPs of the 329-seat body.

On Sunday, lawmakers led by populist cleric Moqtada al-Sadr and Abadi announced they had managed to form an alliance that would give them a majority bloc in parliament.

Hours later, a rival grouping led by militia commander Hadi al-Amiri and former Prime Minister Nuri al-Maliki responded by saying it had formed its own alliance that would be the largest bloc, after it persuaded some lawmakers to defect from the rival group.

Amiri and Maliki are Iran’s two most prominent allies in Iraq. Abadi is seen as the preferred candidate of the United States, while Sadr portrays himself as a nationalist who rejects both American and Iranian influence.

Both groups continued to claim they held the majority on Monday, complicating the election of a speaker.

Iraqis voted in May in their first parliamentary election since the defeat of Islamic State’s self-declared caliphate, but a contentious recount process delayed the announcement of final results until earlier this month.