The opposition Hezbollah movement says it wants to return Lebanon to the situation it was in before its battles with government supporters Hezbollah seizes large parts of Beirut ...
More Arab leaders boycott summit ... last week.
On Wednesday, the government retracted two key measures aimed at curbing Hezbollah which triggered the clashes.
Arab League mediators met both sides in Beirut in an effort to bring an end to the violence in which at least 60 people were killed.
Hezbollah did not say whether it would end its blockade of Beirut airport.
However, airport officials said the national carrier MEA would resume international flights to the airport later on Thursday.
The deputy leader of the mainly Shia political and militant movement, Naim Qassam, told a news conference that Hezbollah would return the situation in Lebanon back "to normal", without specifying what he meant.
Climb down
Eyewitnesses said many roads were still blocked in Beirut after Mr Qassam's statement, which was broadcast live on television.
The BBC's Crispin Thorold in Beirut says the government in effect backed down, retracting demands the head of airport security be moved from his job and Hezbollah's private phone system be shut down.
The network is a key element of the Hezbollah's military capability and what it calls the "weapons of resistance" against Israel.
Arab mediators are set to unveil a new negotiation plan which will include an end to what officials called a civil disobedience campaign by Hezbollah.
The Hezbollah-led opposition left a national unity coalition cabinet late in 2006, demanding more power and a veto over government decisions.
The deadlock has stopped parliament from electing a new president for more than six months, creating an unstable power vacuum.
(BBC)
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