The clashes fed into a growing political crisis in Lebanon linked to the civil war in neighbouring Syria.
Opposition leaders and their supporters accuse Syria of being behind the car bombing that killed Brigadier General Wissam al-Hassan on Friday. They say Mikati is too close to Syrian President Bashar al-Assad and his Lebanese ally Hezbollah, which is part of Mikati's government.
Thousands turned out in downtown Beirut's Martyrs' Square for Hassan's funeral, which also served as a political rally. The violence erupted after an opposition leader demanded that Mikati step down to pave the way for talks on the crisis.
A group marched to the prime minister's office, then overturned barriers, pulled apart barbed wire coils and threw steel rods, stones and bottle at soldiers and police.
Security forces responded by shooting into air and firing teargas, forcing the protesters to scatter.
On Sunday night, gunmen armed with rifles and rocket-propelled grenades exchanged fire in southern districts of Beirut, security sources said, and residents could hear the sound of ambulance sirens.
There were no immediate reports of casualties from the clashes in the capital, but in the northern city of Tripoli a 9-year-old girl was killed by a sniper and several people were wounded in clashes.
Gunmen have been patrolling the streets in Tripoli, scene of previous clashes between Sunnis and Alawites sympathetic to different sides in the Syria war.
Opposition leader Saad al-Hariri urged supporters to refrain from any more violence.
"We want peace, the government should fall but we want that in a peaceful way. I call on all those who are in the streets to pull back," Hariri said on the Future Television channel.
SECTARIAN TENSIONS
Sunday's events highlighted how the 19-month-old uprising against Assad has sharpened deep-seated sectarian tensions in Lebanon, which is still scarred from its 1975-90 civil war.
Sunni-led rebels are fighting to overthrow Assad, who is from the Alawite minority, which has its roots in Shi'ite Islam. Lebanon's religious communities are divided between those that support Assad and those that back the rebels.
Hassan, 47, was a senior intelligence official who had helped uncover a bomb plot that led to the arrest and indictment in August of a pro-Assad former Lebanese minister.
A Sunni Muslim, he also led an investigation that implicated Syria and the Shi'ite Hezbollah in the 2005 assassination of Rafik al-Hariri, a former prime minister of Lebanon.
Damascus and Hezbollah have condemned Hassan's killing.
But mourners at Martyrs' Square accused Syria of involvement and called for Mikati to quit. One banner read "Go, go Najib" echoing the slogans of the Arab Spring.
The violence broke out after Fouad al-Siniora, a former prime minister, said the opposition rejected any dialogue to overcome the political crisis caused by Hassan's killing unless the government first resigned.
"No talks before the government leaves, no dialogue over the blood of our martyrs," Siniora said to roars of approval from the crowd.
Mikati said on Saturday he had offered to resign to make way for a government of national unity, but that he had accepted a request by President Michel Suleiman to stay in office to allow time for talks on a way out of the political crisis.
