Clashes also broke out in the northern city of Tripoli, with residents of two neighborhoods that support opposite sides in Syria's civil war exchanging gunfire.
Security officials have said six others were killed in the car bomb on Friday, and scores were wounded. But Lebanon's National News Agency said on Sunday that the final toll death toll was three: al-Hassan, his guard and a civilian woman.
The discrepancy could not be explained, though security officials said the other five victims were counted based body parts found at the blast site.
Al-Hassan headed an investigation over the summer that led to the arrest of former Information Minister Michel Samaha, a Lebanese politician who was one of Syria's most loyal allies in Lebanon.
"He was killed while he was defending his country," said Samer al-Hirri, who traveled from northern Lebanon to attend the funeral.
France's Foreign Minister Laurent Fabius said it was likely that Assad's government had a hand in the assassination.
"Everything suggests that it's an extension of the Syrian tragedy," he told Europe-1 radio.
Sunday's protests quickly overshadowed the stately funeral for al-Hassan and his bodyguard.
Before the funeral, giant posters of al-Hassan were set up around Beirut calling him a "martyr of sovereignty and independence."
Thousands of mourners packed central Martyrs Square as soldiers carried in two flag-draped coffins.
"We came for Lebanon's future to show that we will not be scared," said mourner Rama Fakhouri, an interior designer. Many chanted that al-Hassan was a "martyr" who was struck down while trying to protect Lebanon.
TV footage showed al-Hassan's wife Anna, his young sons Majd and Mazen, and his parents, shedding tears near his coffin.
But the mood quickly changed. At one point, a Sunni cleric, Osama Rifai, gave a fiery speech, telling the crowd not to "be like women" and "take out their swords." Lebanese journalist Nadim Qutaish also called on mourners to "storm the government headquarters."
Both men's comments were carried live on TV and crowds of protesters approached the government headquarters soon after.
Al-Hassan's killing has set off a new round of political wrangling in Lebanon.
Before the clashes, Saniora called on Prime Minister Najib Mikati to resign, calling his Cabinet the "government of assassination."
"Staying in your post means that you approve of what happened," he said, adding that al-Hassan's killers "had domestic help."
Many of Lebanon's Sunnis see Mikati's government as too close to Syria and the Assad regime, which is dominated by the Alawites — an offshoot of Shiite Islam.
A member of Mikati's Cabinet, Ahmad Karami, told the LBC TV station that the prime minister "is not clinging to the post but will not resign under pressure because of the chaos in the country."
Some Lebanese see al-Hassan's killing and Sunday's violence as an extension of Syria's civil war into Lebanon. While Lebanon's Sunnis have largely backed the uprising, many others, especially Shiite Hezbollah, have stood by Assad.
For the protesters, the connection was clear.
"The Syrian regime started a war against us and we will fight this battle until the end," said protester Anthony Labaki, a 24-year-old physiotherapist.
For years after Syria's 2005 pullout from Lebanon, there was a string of attacks on anti-Syrian figures in the country with impunity. Assad managed to maintain his influence in Lebanon in the years afterward through Hezbollah and other allies.
Samaha, the former minister arrested in al-Hassan's investigation, remains in custody. He is accused of plotting a wave of attacks in Lebanon at Syria's behest.
Syrian Brig. Gen. Ali Mamlouk, one of Assad's most senior aides, was indicted in absentia in the August sweep that saw Samaha arrested. Samaha's arrest was an embarrassing blow to Syria, which has long acted with impunity in Lebanon.
Elizabeth A. Kennedy and Barbara Surk contributed reporting from Beirut.
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