"We want these ceremonies to be for the sake of Lebanon's unity and for the sake of the establishment of a Lebanese national unity government," Ali Bezzi, a Shia MP, told the crowds late on Monday.
Lebanon's army has deployed more soldiers in districts that lead to the protest site amid fears Sunday's killing could lead the country into sectarian violence.
The demonstration has been peaceful but the surrounding districts witnessed several clashes between residents and protesters, which has left one dead and others wounded.
The opposition said the incidents would not drive it to abandon plans for toppling the government of Siniora.
The Shia group Hezbollah, which is backed by Syria and Iran, and its allies in the opposition are holding an indefinite sit-in to force Siniora's resignation.
Thousands of protesters have spent four nights in a tent city built in central Beirut outside the main government complex where Siniora and his ministers are spending their days and nights.
The opposition, which includes some Christians, has been demanding effective veto power in the government, which has a majority comprising of anti-Syrian politicians from Christian, Sunni and Druze parties.
Six opposition ministers resigned from the cabinet last month after unity talks collapsed. But the depleted government approved plans for the al-Hariri tribunal, sparking the latest protests.
Al Jazeera's Hashem Ahelbarra reported that several skirmishes between rival protesters were quickly put down by security forces.
Amid the protests, Amr Moussa, secretary general of the Arab League, arrived in Beirut to meet Lebanese officials.
"When they are convinced that there is no solution except through dialogue, then welcome"
Walid Jumblatt, Druze leader
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Moussa said Arab countries could not afford to be bystanders.
He said: "The stability of Lebanon and moving towards a solution that would bring about a sure future for the country is one of our concerns."
"All of us are worried about the situation in Lebanon."
Government supporters, who held their own mass funeral procession following the assassination of Pierre Gemayel, a member of the Lebanese majority coalition, stayed away from central Beirut on their leaders' advice.
Walid Jumblatt, a member of the majority March 14 Forces alliance and de facto leader of Lebanon's Druze Muslim community, said: "We will be steadfast, peacefully and democratically. We are here, and when they are convinced that there is no solution except through dialogue, then welcome."
Despite the protest, the city's annual marathon went ahead. Runners used suburban roads to skirt the demonstration.
The opposition has been demanding veto power in the government, whose majority comprises politicians from Christian, Sunni Muslim and Druze parties.
Hezbollah receives financial and logistical support from Iran and Syria, while most members of the majority March 14 Forces coalition are opposed to Syrian influence in Lebanon.
Syrian troops and security pulled out of Lebanon in April 2005 following street demonstrations in the wake of the assassination of Rafiq al-Hariri, a former Lebanese prime minister.
Politicians in the majority coalition say the opposition only wants to weaken the government and derail a UN tribunal that would try those suspected of involvement in the al-Hariri killing.
A preliminary UN inquiry has implicated Syrian and Lebanese security officials in the killing.
Six opposition ministers resigned from the cabinet last month after talks on national unity collapsed. But the depleted government approved plans for the tribunal, leading to the latest protests.