Speculation still surrounds the question of who carried out Monday's bombing in downtown Beirut, which killed al-Hariri and at least 12 other people.
Aljazeera's director in Lebanon, Ghassan bin Jiddo, said the situation in Beirut on Monday night was very tense.
Although the night passed calmly, the army was put on high alert.
Lebanon began three days of official mourning on Tuesday, with schools, shops, private and public institutions all closed.
Bin Jiddo said many checkpoints and security forces had been deployed in the city, but there was an incident on Monday night when protesters hurled stones at the Baath party headquarters in al-Kula area and burned pictures of Syrian President Bashar al-Asad.
The Lebanese opposition held a meeting on Monday night at al-Hariri's house.
Jumblatt has told Syrian troops
in Lebanon to leave
Aljazeera's bin Jiddo said they believed the Syrian-backed Lebanese authority was responsible for killing al-Hariri, either directly or by inciting others to kill him.
He added that the opposition had adopted a policy of political escalation against the Lebanese and Syrian authorities.
In a statement, opposition leaders demanded the government resign and Syria completely withdraw its 14,000 troops stationed in Lebanon.
Druze leader Walid Jumblatt, who has previously called for a Syrian withdrawal from Lebanon, said: "Despite the blood and the sadness, we want to tell them: 'We don't want anything from you, go away, leave us, enough blood'."
The opposition called Monday's meeting an open national conference and demanded an international investigation into the blast.
UN Secretary-General Kofi Annan said he hoped the killing would not reignite civil war.
"It is imperative that the already fragile situation in the region should not be further destabilised," Annan's spokesman Fred Eckhard said.
"It is imperative that the already fragile situation in the region should not be further destabilised"
Fred Eckhard, spokesman for UN Secretary-General Kofi Annan
The US said it would consult UN Security Council members about punitive measures.
The council planned a formal meeting on Tuesday on the killing as well as on its resolution demanding Syrian troops leave Lebanon.
On Tuesday, the Lebanese As-Safir newspaper published what it said were al-Hariri's last public words, said to reporters at a cafe outside parliament, minutes before his death.
"Mistakes have been made and are still being made," he said.
"I don't see that as being in the interest of the country. Everyone should realise that Lebanon cannot continue without an internal national accord and one with Syria."
In a videotape broadcast by Aljazeera, a previously unknown group calling itself al-Nusra wa al-Jihad fi Bilad al-Sham (Victory and Jihad in Palestine, Jordan, Lebanon and Syria) claimed responsibility for the assassination, which it said was due to al-Hariri's support for the Saudi royal family.
However, unconfirmed reports said the group later denied involvement on a website.
The authenticity of both the video and web statement could not be verified.
Meanwhile, Muhammad al-Qabbani, a representative of al-Hariri's opposition coalition, told Aljazeera: "The family has decided to hold a public funeral, as we don't want an official one in which the authorities participate.
"Mistakes have been made and are still being made. I don't see that as being in the interest of the country. Everyone should realise that Lebanon cannot continue without an internal national accord and one with Syria"
Former prime minister Rafiq
al-Hariri's reported last words
"Therefore, the funeral will be held on Wednesday starting from his house in Quraitim area. We will then go to the significant Muhammad al-Amin mosque where the prayer for the dead will be performed, so the body can be buried there."
Al-Qabbani dismissed claims that a ministerial committee has been formed to prepare for a national funeral procession.
"This is not our business. We will organise a public funeral procession, with the participation of ordinary people, just like what al-Hariri has always wanted.
"We know that some international top officials, like French President Chirac, may attend the funeral. We welcome them in al-Hariri's house and Muhammad al-Amin mosque."
Syrian Vice-President Abd al-Halim Khaddam offered his condolences to al-Hariri's family, Aljazeera's correspondent in Lebanon reported.
Israel on alert
Israel said on Tuesday it was on alert for a possible rise in violence on its border with Lebanon following the assassination.
"We have to be vigilant because this assassination could cause instability in Lebanon that could be exploited" by anti-Israeli elements, a senior aide to Prime Minister Ariel Sharon said.