Lebanese Prime Minister Najib Mikati said he has offered his resignation but that President Michel Suleiman has asked him to stay on for a "period of time".
Lebanon's opposition March 14 bloc had called for the government to resign after yesterday’s bomb attack in Beirut.
A prominent Lebanese intelligence official opposed to Syrian President Bashar al-Assad was among those who died.
Protesters and gunmen blocked roads with burning tyres in Beirut and other cities over the attack.
Lebanese soldiers opened fire on a group who took over a road in the Bekaa valley, wounding two people, witnesses said.
Troops reinforced road junctions and official buildings in the capital but many roads, including the highway to the international airport, were cut off by demonstrators.
The protests broke out in reaction to the killing of Brigadier-General Wissam al-Hassan.
Politicians accused President Assad of being behind the attack, deepening fears that the sectarian-tinged civil war in neighbouring Syria is spilling over into Lebanon.
Mr Hassan had led an investigation that implicated Syria and its Lebanese ally Hezbollah in the assassination of former prime minister Rafik al-Hariri in 2005.
He had also helped uncover a bomb plot that led to the arrest and indictment in August of a pro-Assad former Lebanese minister - a setback for Syrian influence in Lebanon.
The Beirut Star newspaper said the perpetrators of the bombing, which killed at least eight people and wounded more than 80, clearly aimed to push Lebanon into a new round of chaotic violence.
US Secretary of State Hillary Clinton said Mr Hassan's killing was "a dangerous sign that there are those who continue to seek to undermine Lebanon's stability".
French President Francois Hollande urged Lebanese politicians to stay united and prevent attempts to destabilise the country.
The Vatican and the European Union also condemned the attack.