Mohsen Hakim, son of party founder Abdul Aziz al-Hakim and a senior adviser, said no formal date was set but expressed optimism any future meetings between the two neighbors would yield positive results.
Baghdad wanted to move forward to resolve any open issues with Tehran to address security conflicts and sovereignty issues, Hakim told The Tehran Times.
He called the latest visit to Iran by a delegation handpicked by Maliki "constructive and fruitful," adding Tehran expressed its support for the Maliki government on "political, economic and security" issues.
The invitation comes on the heels of statements from Iranian officials saying any further talks with Washington while violence escalated in Baghdad were out of the question.
"In view of the U.S. open bombing and the assault of the Iraqi nation, Iran-Iraq-U.S. trilateral talks would be meaningless," Iranian Foreign Ministry spokesman Mohammad Ali Hosseini said.
"The trilateral talks require a special psychological climate where all sides believe in the main purpose of the discussions. … If one of the three sides lacks this belief, the negotiations will face serious problems," he added.