"In order to avoid multiple efforts, we have decided to form a committee that would preserve a role for Sunnis in the next government," he said on Monday.
Apart from the symbolic position held by al-Yawir, Sunnis, who once dominated Saddam Hussein's government, currently have eight of the outgoing government's cabinet seats.
Sunnis garnered only 20 of the 275 seats in the newly-elected parliament due to a boycott of the 30 January elections by large segments of the community.
The al-Yawir bloc includes figures such as elder statesman Adnan al-Pachachi and Tariq al-Hashimi, secretary-general of the Iraqi Islamic Party (IIP), which had officially pulled out of the elections.
The Shia and Kurds who swept the elections are currently locked in hard bargaining over the composition of the next government.
Both have said they were eager to include the Sunnis and avoid alienating them, especially as most of the anti-government and anti-US fighting has been concentrated in Sunni areas such as Mosul, Samarra and al-Anbar province.
"In order to avoid multiple efforts, we have decided to form a committee that would preserve a role for Sunnis in the next government"
Separately, the monarchist movement headed by the once-exiled Sharif Ali bin al-Hussein, one of the heirs to the overthrown Iraqi monarchy, met on Monday with the representatives of the influential Association of Muslim Scholars.
"The Association maintains its position: We will not take part in the government as long as the country is under occupation," said its chief Harith al-Dhari.
"But we do not oppose those who want to take part to serve the country and pull it out of its misery."
The monarchists, who took part in the elections without winning seats, said they are willing to join the government.
"I am willing to accept any post to serve the people," said al-Hussein.