Muhannad al-Issawi, a spokesman for Adnan al-Dulaimi, leader of the Iraqi Accordance Front, had said that 44-seat bloc decided in a meeting Saturday to demand that al-Mashhadani preside over Sunday's session.
"If the demand is rejected by other blocs, then the Accordance Front will suspend its participation in parliament," al-Issawi had told The Associated Press.
The Accordance bloc was joined in the boycott by the 11-seat National Dialogue Front.
The Sunni boycott threatens to further disrupt the work of Prime Minister Nouri al-Maliki's Shiite-dominated government as it seeks to enact legislation, under pressure from the United States, to reconcile the differences among Iraq's Shiite, Sunni and Kurdish groups.
The Accordance bloc is a participant in the al-Maliki coalition, which already had been undermined by a boycott by the 30-seat Shiite bloc of anti-American cleric Muqtada al-Sadr. The National Dialogue Front is not part of the government.
Parliament voted June 11 to ask al-Mashhadani, a Sunni Arab, to step down and assigned his deputy, Shiite Khaled al-Attiya, to his place until a permanent replacement was found. It also asked the Accordance Front, to which the speaker belongs, to name a replacement within a week.
Al-Mashhadani repeatedly has embarrassed the Sunni Arabs in al-Maliki's Shiite-dominated coalition government. Many legislators viewed his behavior as unbecoming and occasionally erratic.
A senior lawmaker from the Accordance Front, Salim Abdullah, had said his bloc would return to parliament only if al-Mashhadani is reinstated and a law defining the legal and constitutional grounds for the dismissal of the speaker was adopted.
The Sadrist bloc declared a boycott to protest against what they say was the government's failure to protect a key Shiite shrine north of Baghdad. It was bombed June 13 for the second time in less than 16 months.
With the three blocs boycotting, the parliament would have to hold sessions with only 190 legislators, assuming that all the remainder attend. While 190 would fulfill a quorum of 138, the boycott would cast a shadow over any major legislation.
Some of the Accordance Front lawmakers voted in favor of ousting al-Mashhadani in the June 11 vote, but the bloc appears to have adopted a hardline stand on the issue following a series of meetings. Lawmakers from the bloc have refused to say how many of them voted in support of his ouster. The media was banned from the session in which the vote was taken.
The Accordance Front is made up of three parties — the moderate Islamic Party and the hardline Congress of the People of Iraq and al-Mashhadani's National Dialogue Council.
Al-Mashhadani has not been inside the chamber since the vote, but has been to his office and continues to retain a large security detail. He has defended himself in a series of television interviews over the past two weeks, insisting that his ouster was unconstitutional.
He has said he was named speaker as part of the same sectarian, power-sharing deal that gave Jalal Talabani, a Kurd, the presidency and al-Maliki, a Shiite, the prime minister's job.