The talks got under way at the Sheraton hotel in Doha.
Addressing Lebanese leaders at the opening session, Al-Thani said: "Dear brothers, I am delighted to welcome you here in Doha ... representatives of all the Lebanese forces or envoys of Arab countries or organisations which are concerned about what is going on in Lebanon [and] all [who] want to protect its future by maintaining its unity."
"I hope that you reach an agreement to avert dangerous consequences [in] hard times that threaten a country which we are all demanded to maintain and protect."
The government and the Hezbollah-led opposition agreed a day earlier in Beirut, Lebanon's capital, to a new national dialogue to elect a president and form a unity government.
Al Jazeera's Rula Amin reported that there was a lot of hope that the talks would yield positive results, though it would be difficult to make the different factions agree.
"People have a lot of hope that it will work. However, they know that the issues are real. The political factions that are here have different interests, different concerns and have different visions for Lebanon. So it is not an easy job to bring them all together and to get them agree in a short time as well," Amin said.
"Only a week ago, these leaders were talking to each other through the guns and there were bloody clashes between their supporters on the streets. However, there seems to be a will, not only among the Lebanese factions but also from the regional Arab countries and Iran, that this crisis has to be contained and an end to the violence has to be put."
Earlier, a six-point plan was approved on Thursday under the mediation of an Arab League delegation headed by Sheikh Hamad bin Jassim al-Thani, who is both Qatar's prime minister and foreign minister.
Under the deal, the rivals undertook to launch a dialogue "to shore up the authority of the Lebanese state throughout the country", to refrain from using weapons to further political aims, and to remove fighters from the streets.
It also called for the rivals to refrain from using language that could incite violence, as well as the removal of roadblocks that have prevented access to Beirut airport and other parts of the country.
Shortly after the six-point plan was announced, the opposition cleared a series of roadblocks leading to Beirut airport.
Air traffic came in to land at the airport shortly afterwards.
The Arab League intervention was prompted by the worst sectarian violence since the 1975-1990 civil war, marked by the takeover by opposition fighters from Hezbollah and its allies such as the Amal of large swaths of west Beirut.
Hopes of a deal were raised on Wednesday after the Siniora government cancelled two measures against the Hezbollah that were seen as the trigger for the latest unrest.
The cabinet rescinded plans to investigate a private Hezbollah phone network and reassign the head of airport security over allegations that he is close to Hezbollah.
Hassan Nasrallah, the Hezbollah chief, had branded those moves a declaration of war.
Parliament in Beirut is scheduled to convene on June 10 for its 20th attempt to elect a president.
Both sides agree on General Michel Suleiman, the army chief, as the new president, but they remain divided over the details of a proposed unity government and a new law for parliamentary elections due next year.
Six opposition ministers quit the Siniora cabinet in November 2006, sparking the current political crisis.
Thursday's announcement in Beirut said the Doha dialogue would also lead to the end of a long-running opposition sit-in that has left the heart of downtown Beirut a virtual ghost town.
The latest developments coincide with a visit to the region by George Bush, the US president, who has accused Hezbollah and its Iranian and Syrian allies of setting out to destablise the country.