Asked to confirm that stance publicly on television on Tuesday, the party general secretary kept to a more cautious line, saying it would probably drop its opposition to the charter if it had legal confirmation of the changes it wanted.
The party source said after a day of meetings with leaders from the ruling Shia and Kurdish coalition: "Some of our demands were met so the party has endorsed the constitution and is urging people to vote yes."
He said he expected a formal announcement to be made at the residence of President Jalal Talabani on Wednesday.
Sources said Iraqi government negotiators agreed to a key demand from minority Sunni Arabs that parliament should review possible amendments to the constitution four months after December's election.
A Talabani spokesman said talks were continuing to define which articles of the constitution, set to be voted on in a referendum on Saturday, would be reviewed and a formal announcement was expected on Wednesday.
"There's a basic agreement to amend the constitution," he said. "They are now looking at what points to review."
Ayad al-Samarraie of the Iraqi Islamic Party said that if the current parliament approves the measure, "we will stop the campaign rejecting the constitution and we will call on Sunni Arabs to vote yes".
There was no agreement, however, about precisely how the constitution might be amended, leaving the Sunni Arab minority still at risk of being disappointed in next year's negotiations.
The Shia deputy speaker of parliament, Hussain Shahristani, said he expected Sunni Arabs, who mostly boycotted a January election that then sapped their power to influence negotiations on the constitution in parliament, to take part in large numbers in a general election expected on 15 December.
Hussain Shahristani expects Sunni
Arabs to vote at December polls
"These discussions are mainly useful so that ... they can as of now study amendments and discuss them" for debate in the new National Assembly that will sit next year, he said.
US diplomats have been working hard to bring the sides to an agreement to prevent the Sunni Arab minority, dominant under Saddam Hussein, from turning more heavily to violence that has ravaged the country for two years.
Arab League effort
An influential Sunni Muslim group on Tuesday said it was ready to take part in a national reconciliation conference called for by the Arab League but stipulated conditions.
The secretary general of the Association of Muslim Scholars, Shaikh Harith al-Dhari, after meeting the Arab League delegation, listed the group's conditions as a timetable for the pullout of foreign forces, a definition of terrorism and recognition of the Iraqi resistance as well as an effort to reinstate the Iraqi army.