Talks between the two sides are to continue in the Qatari capital Doha today, with the ambitious aim of reaching a deal to end months of political paralysis.

Beirut airport, blockaded for a week, was being reopened last night after Sheikh Naim Qassim, deputy leader of the Iranian-backed Shia militia, pledged to return the situation "to normal". Ordinary Lebanese expressed relief at the easing of tensions that brought reminders of a bloody past.

Agreement was reached after a climbdown on two issues by Fuad Siniora, the Sunni prime minister. Last week he challenged Hizbullah by sacking the head of security at Beirut airport, allegedly a sympathiser, and calling its private communications network illegal. Hizbullah insisted its communications were an essential part of its ability to fight Israel.

The government tried to save face by saying it was placing the two issues in the hands of the Lebanese army, a neutral force which failed to intervene in last week's clashes, with at least 80 dead and 250 injured in the worst internecine fighting since the 1975-90 civil war.

"The government has wisely withdrawn the controversial decisions that sparked the crisis," said Patrick Haenni of the International Crisis Group. "Now the onus is on all Lebanese parties to de-escalate the situation and reach a broader political accord."

Sheikh Hamad bin Jassem, the Qatari prime minister, announced the agreement flanked by Amr Moussa, secretary general of the Arab League. "The parties pledge to refrain from returning to the use of weapons or violence to achieve political gains," Hamad said.

Nadim Shehadi, an analyst at London's Chatham House thinktank, argued: "It's not a humiliating climbdown because the government has succeeded in highlighting the illegality of the situation. The government can't fight Hizbullah militarily. It can only do so politically."

Privately, though, Siniora's supporters are dismayed at this turn of events, with the only comfort that Hizbullah has clearly damaged itself by turning its weapons on fellow Lebanese.

The government did exercise restraint but it had little choice, since - the army apart - it has no armed force capable of taking on Hizbullah, other sectarian militias having been disbanded.

It was unclear whether the agreement would be a first step towards breaking the impasse between the government and the opposition, which has left Lebanon without a president since the pro-Syrian incumbent left office last November. General Michel Suleiman, the army commander, is the compromise candidate.