Al-Sadr loyalists walked out of their positions in parliament and the cabinet after Nouri al-Maliki, the Iraqi prime minister, met Bush in Jordan three weeks ago.
Two figures in al-Sadr's movement, an aide to the cleric and a member of Iraq's parliament, also said the cleric had agreed to allow his followers to rejoin the government.
"We will rejoin the government and the parliament very soon," the parliament member said, speaking on condition of anonymity because of the sensitivity of ongoing meetings.
"We have some guarantees during our meeting today," he said.
On Thursday, al-Sadr's loyalists met with members of the Shia bloc, and laid out their demands for returning to the government, the official said.