Shia politicians in Iraq have been discussing the future of the governing alliance in the city of Najaf.
The governing alliance want the influential Sadr back in the fold
They want to persuade radical cleric Moqtada Sadr to rein in his militia and rejoin the political process.
The walk-out was in protest at a meeting between Prime Minister Nouri Maliki and US President George W Bush.
A faction spokesman said the boycott of government and parliament would stay until its demand for a timetable for a US-led troop withdrawal had been met.
Shia leaders met in Najaf as part of consultations with the country's most prominent Shia cleric, Ayatollah Ali al-Sistani.
They want to form a new governing coalition that will bring together the main Shia parties and representatives of Sunni Arab and Kurdish groups.
Dr Ali al-Adib, a member of the Shia Dawa party, said on Thursday that the Shia bloc planned to tell Ayatollah Sistani about the political process, a cabinet reshuffle and the security situation.
He told the Associated Press news agency the leaders would also ask Mr Sadr "to end the boycott and return to the political process".
The elderly Ayatollah Sistani is revered by most of Iraq's Shias. He has considerable influence among the Shia parties but has eschewed any personal political role.
Iraq's Shia-dominated government seems very keen to see Moqtada Sadr return to the political fold.
About 30 of his loyalists walked out of the Iraqi parliament when Mr Maliki met Mr Bush in Jordan three weeks ago.
The move was a blow for the government and illustrated the huge influence the young cleric wields in the country.
The delegation of politicians which visited Najaf on Thursday came from the seven factions of the Shia alliance which make up the largest government bloc.
They are also calling on Moqtada Sadr to rein in his militia, the Mehdi Army, which is accused of taking part in sectarian attacks in Iraq. But there is no news of progress on that issue.