The meeting came a day after Al-Hashemi published a proposal that he said would help achieve reconciliation in Iraq.
The document calls for a blanket pardon for Iraqis who took up arms against the government and the US-led coalition in exchange for laying down their arms and joining the political process.
Al-Hashemi, who is also head of the Iraqi Accord Front, told reporters after the meeting that the two sides discussed the political situation in Iraq and the way out of current political standoff.
Al-Hashemi said that the front presented a proposal, including twenty-five points, to Ayatollah Sistani.Al-Hashemi's party is part of a Sunni political alliance in Iraq and he is also a one of high-ranking Sunni political figures that has visit Ayatollah Sistani.
The vice president noted that Ayatollah Sistani is acknowledging the situation of Iraq and problems of people in this war-shattered country.
Al-Hashemi said, "Ayatollah Sistani welcomed the meeting and stressed the discussions should be continued in the near future".
Al-Hashemi noted that he briefed Ayatollah Sistani about the reasons behind the pullout of his Sunni political alliance from government of Prime Minster Nouri al-Maliki as well.
"We decided to brief Ayatollah Sistani on situation and decisions in premiership frequently in the future", Al-Hashemi said.
"The time has come to sit around the table and have a candid dialogue about key and sensitive matters," he said.
