The Sovereignty Alliance - a Sunni political coalition - and the Kurdistan Democratic Party told Kadhimi that they would not attend talks that were meant to take place Thursday if the Sadrist movement was not present, The New Arab's Arabic-language sister site Al-Araby Al-Jadeed reported, citing "Iraqi political sources".
The Kurdish and Sunni groups said a new meeting could exacerbate protests from the talks' opponents and would not yield any results, according to the sources. The first round of dialogue took place last week without the Sadrists but proved fruitless.
The sources added that Hadi al-Amiri, the leader of the Fatah alliance that is part of the Coordination Framework coalition of Shia parties that oppose the Sadrists, told Kadhimi that some members of his umbrella group are boycotting the talks.
The boycotting parties say that Kadhimi is in no position to hold the dialogue as they do not consider him to be a neutral party in the crisis.
The situation prompted Kadhimi to inform participating parties that the talks were being postponed, the sources said, with no new date for talks given.
Efforts to persuade parties to take part would continue.
The Sadrists were the biggest winners in Iraq's parliamentary election, which took place almost a year ago.
Sadr and the Coordination Framework have been at odds since after last year's parliamentary elections. The Sadrists won the largest share of seats in the October vote but failed to form a majority government.
MPs belonging to Sadr's bloc later resigned from parliament and his supporters last month stormed the parliament building in Baghdad. He has demanded that parliament be dissolved and early elections held.
The Coordination Framework said earlier that parliament would have to convene to dissolve itself.
For a month, Sadrist movement supporters have held sit-ins, first inside the legislature and later on its surrounding grounds.
In response, Coordination Framework supporters said they would hold an "indefinite sit-in" to counter Sadrist protests and push for the swift formation of a new government.
Supporters of the Sadrist movement on Tuesday began a sit-in in front of the Supreme Judicial Council headquarters in Baghdad's Green Zone to demand parliament's dissolution and judicial reform.
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