"We pledge that the blood of Rafiq Hariri and his comrades will not have been shed in vain and we will not spare any effort to unmask those who ordered this crime, no matter their position," a family statement said on Thursday.
Al-Hariri and 17 others were killed in a massive explosion on Monday that officials said could have been caused by a car bomb.
"We call on the Arab and the international communities to implement the declaration of the president of the Security Council ... to identify and punish the culprits within a short and reasonable time," the family said.
Government under pressure
Meanwhile, Lebanon's government is coming under growing pressure to solve the assassination.
French President Jacques Chirac demanded that "light be shed" in the murder of his friend, al-Hariri, as he flew to Beirut on Wednesday to pay his respects to the family and at the grave.
Seventeen other people died in the
blast that killed al-Hariri
US Secretary of State Condoleezza Rice, testifying at a Senate hearing, said "there needs to be an international investigation" of the killing, echoing an earlier call from Chirac.
But a State Department official said Rice was not, at this point, going beyond a UN Security Council move to ask Secretary-General Kofi Annan to report on the "circumstances, causes and consequences" of the killing.
Rice said the US was working with its partners in the UN, particularly France, on the follow-up to the slaying and she had spoken with French Foreign Minister Michel Barnier.
Since the outbreak of its 1975-1990 civil war, Lebanon has had a long list of unresolved assassinations, many of them similar in circumstances to the killing of al-Hariri.
Lebanon decided on Wednesday to seek the help of Swiss experts to investigate the killing of al-Hariri, judicial sources said. Aljazeera learned that Lebanon rejected a French offer of help in the inquiry.
"We pledge that the blood of Rafiq Hariri and his comrades will not have been shed in vain and we will not spare any effort to unmask those who ordered this crime, no matter their position"
Statement from al-Hariri's family
An examining magistrate of Lebanon's military tribunal, Rashid Mizhir, called for the assistance of Swiss experts specialised in explosives and DNA, the sources said.
Lebanon's Interior Minister Sulaiman Franjiya has rejected calls for an international inquiry but not ruled out a role for foreign expertise from "neutral countries".
France and the US sponsored a UN Security Council resolution September that called for Syria to withdraw its troops deployed in Lebanon.
The top US envoy to the Middle East, William Burns, called in Beirut for the "complete and immediate" withdrawal of Syrian troops from Lebanon and demanded a "credible" investigation into the assassination.
Burns has called for the complete
withdrawal of Syrian troops
The US, while stopping short of directly holding Syria responsible, has recalled its ambassador from Damascus for consultations and warned of deteriorating ties, although Damascus insists it had no role in the killing.
Al-Hariri, who served as premier five times since the end of the civil war, resigned in October over what he said was Syria's domination of Lebanon.
Government offer spurned
His family had called for a massive public turnout, spurning a government offer to hold a state funeral and demanding that no officials from the Syrian-backed government attend.
Lebanon's opposition has said that the Beirut authorities and Damascus were involved in the assassination.
Anger at al-Hariri's death turned violent on Wednesday when a group of people hurled stones at Syrian workers and beat them up in al-Hariri's southern hometown of Sidon, in the second such incident in two days.
Lebanon has come to a virtual standstill since the assassination, with the government calling for a period of mourning and the opposition a general strike, both of which were to end on Friday.