Lebanese soldiers opened fire on a group who took over a road in the Bekaa valley, wounding two people, witnesses said.
Troops reinforced security at junctions and official buildings in the capital but many roads, including the highway to the international airport, were cut off by demonstrators.
The protests were a reaction to the killing of Brigadier-General Wissam al-Hassan in a car bomb attack in central Beirut on Friday afternoon, in which at least seven other people died and more than 80 were injured.
Lebanese Prime Minister Najib Mikati said yesterday he had been asked by the president to stay in his post as tension in the country grew.
Mikati told a news conference that he had offered his resignation to President Michel Suleiman to make way for a government of national unity, but had been asked to remain in office for the time being.
Politicians accused Syrian President Bashar-al Assad of being behind the assassination, deepening fears that the sectarian-tinged civil war in neighbouring Syria is spilling over into Lebanon.
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 of a pro-Assad former Lebanese minister.
Lebanon's religious communities are divided between those that back Assad in Syria's civil war and those that support the Sunni-led rebels.
In Beirut's Sunni Muslim areas, where people are opposed to the Alawite Assad, cars mounted with loudspeakers cruised the streets issuing calls for the Lebanese government to resign.
Gunmen were in the streets and the mood was tense, witnesses said. Squads of gunmen were also in the streets in the northern, mostly Sunni city of Tripoli, where pro- and anti-Assad factions clashed this year. Rallies were also held and roads closed in the eastern Bekaa Valley and in the southern town of Sidon.
Soldiers and police guarded street corners in Beirut's Ashrafiyeh area, the mainly Christian district where the bomb exploded at rush hour, and at Martyrs' Square in the centre.
Lebanon's mufti, the senior Sunni religious figure, announced three days of mourning for Hassan. He will be buried with full honours today.
The Beirut Star newspaper said the perpetrators of the bombing clearly aimed to push Lebanon into a new round of chaotic violence.
"If the goal was to divert attention from the events in Syria, then people should remember this well and head off any attempt to take Lebanon further into tension and civil strife," it said.
Saad al-Hariri, the son of the late prime minister, accused Assad of being behind the bombing.
Lebanon's opposition March 14 bloc called on Prime Minister Mikati's government, which includes ministers from Hezbollah, to resign.
The head of Lebanon's Internal Security Forces, Major-General Ashraf Rifi, described Hassan's death as a "huge blow" and warned further attacks were likely.
"We've lost a central security pillar," he said. "Without a doubt, we have more sacrifices coming in the future. We know that, but we will not be broken."
The bombing also heightened fears in the West that Syria's war could ignite conflict across the region.
US Secretary of State Hillary Clinton said 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.
Augustus Richard Norton, a Middle East specialist at Boston University, said it was too early to say who carried out the bombing.
"However, there is no doubt that al Hassan's death will bring smiles to the face of Bashar al-Assad and his cohorts," he wrote in a commentary.