Discussing the necessity of holding free and fair elections on time on Tuesday, Birri - who said he was first surprised by Jumblatt's visit - expressed his wish that the meeting was the "beginning of reconciliation between both parties".
Jumblatt also stressed the need for cooperation. "The assassination of former prime minister Rafiq al-Hariri created a tension that split the country in two - the loyalists and the opposition."
He added that the opposition's demands were being met in accordance with the Taif Accord.
"The Syrian withdrawal took place according to the Taif Accord and concerning the international investigation [on al-Hariri's assassination] it seems that the decision will come out soon, and both were among the opposition's demands," said Jumblatt.
But he also commented on a third opposition demand regarding elections, emphasising that any ballot was "an internal issue that should only be dealt with internally".
UN envoy view
Jumblatt's comments come as UN special envoy Terje Roed-Larsen also called for Lebanese elections to be held on schedule.
Visiting military sites abandoned by the withdrawing Syrian army, the envoy stressed the need for organisations such as Hizb Allah to disarm.
But Aljazeera learned that the Lebanese government is opposing this demand because it says the issue contradicts the Taif agreement. Jumblatt has also said disarming Hizb Allah is not a priority at this time.
Commenting on the Syrian pullout, Roed-Larsen said Damascus appeared to be honouring its commitment to withdraw military and security forces from Lebanon.
In remarks that contrasted with US Secretary of State Condoleezza Rice on Tuesday, Roed-Larsen said although a UN team would visit Lebanon to verify the withdrawal within days, he was satisfied that Damascus was pulling its forces out.
Rice told journalists that Syria had to go beyond its stated intention to withdraw troops and security forces from Lebanon, and remove "undeclared" security forces as well.