Sheikh Hamad bin Jassim bin Jabr Al-Thani, the Qatari foreign minister, said that "there are no winners in this conflict".
Speaking at a press conference, he said: "We need Lebanon's help in this, and we will continue to push for a resolution."
"The issues will continue to be expressed in the spirit of dialogue, and I hope all sides with agree with the conditions that will bring an end to the conflict."Airport 'open'
Lebanon's opposition groups also began removing roadblocks on the highway leading to Beirut's international airport, paving the way for commercial flights to resume.
A Middle East airlines (MEA) plane was set to arrive at the airport in the early evening, the first commercial flight since incoming and outgoing flights were suspended a week ago.
"An MEA flight from Paris is scheduled to arrive at 7pm (1600 GMT) and will depart to Larnaca, Cyprus, at 8.30pm," an airport official said.
Lebanon's only international airport has been closed since last Thursday due to the ongoing unrest, the worst to affect the country since the end of the 1975-1990 civil war.
James Bays, Al Jazeera's correspondent, reported from Beirut: "We are hearing that they've made extraordinarily good progress, not just on the current issue of trying to resolve the violence ... we hear the agreement may go much further.
"I understand those talks [in Doha] will look at ways of forming a national unity government, it will look at the electoral law and it will look at a way that they can finally elect a president."Contentious issues
Al Jazeera's Rula Amin, also reporting from Beirut, said that the ruling coalition will press on the issue of Hezbollah's arms and weapons.
|Roadblocks towards Beirut's international|
airport are being cleared [AFP]
She said: "The government wants one more item to be placed on the agenda - the weapons of Hezbollah, and the militia's right to have these weapons.
"This is a contentious issue that will provoke long-winded debate."
Earlier, Sheikh Naim Kassem, Hezbollah's deputy leader, said the group would "return things to normal" after the government reversed decisions that had triggered the conflict.
The roadblocks, including barricades on the airport road, are also expected to be lifted on Thursday.
The row has paralysed much of government and left Lebanon with no president since November.
Analysts believe that behind the dispute is a regional struggle for influence between Syria, which backs the opposition, and Saudi Arabia, which supports the ruling coalition.
Any deal would likely result in General Michel Suleiman, the army commander, being elected president.
The US has blamed the trouble in Lebanon on Iran, Syria and Hezbollah.
Iran blames the US for the violence which erupted after government action to outlaw a communications network vital to Hezbollah's military and security wings.
The ruling coalition accuses the opposition of trying to restore Syrian control of Lebanon and secure a stronger foothold for Iran in the country.
Syria dominated Lebanon until 2005, when the assassination of Rafiq al-Hariri, the late prime minister, triggered international pressure that forced it to end its military presence after nearly three decades and plunged Lebanon into crisis.