Peter Fitzgerald, the head of a three-member UN team, started the investigation by holding meetings with Lebanese officials.
The Lebanese government has insisted that it lead the inquiry but has expressed willingness to cooperate with foreign investigators.
"I look forward to working closely with the Lebanese authorities, and to learning about their progress in investigating this terrible crime. We will also seek to speak to others who might assist us to fulfil our mandate," he said on Friday.
Fitzgerald, also Ireland's deputy police commissioner, said in a prepared statement: "We fully understand the gravity of the task at hand, and can assure all concerned that we will work with absolute impartiality and professionalism."
Fitzgerald said he would not be making any further public statements.
The Irish investigator was expected to visit the seafront street where a powerful bomb hit al-Hariri's motorcade, killing 17 people and injuring more than 100.
Al-Hariri's murder sparked anti-
The team was dispatched by UN Secretary-General Kofi Annan in response to a request from the Security Council that he urgently report on "the circumstances, causes and consequences" of al-Hariri's killing.
Fitzgerald said he hoped to report to Annan on the team's findings in four weeks. He praised the Lebanese government's pledge to cooperate with the team.
Also on Friday, visiting British Foreign Office Minister Baroness Symons urged cooperation in the inquiry and expressed hope it would "shed light on the circumstances of this attack and identify and bring to justice those responsible for it".
She spoke to reporters after meeting with Lebanese Foreign Minister Mahmud Hammud.
Lebanon has promised its own thorough investigation and has asked Switzerland to send DNA and explosives experts to help.
Al-Hariri's family and opposition groups, along with the United States, France and the European Union, have demanded an international investigation to identify the assassins who killed the politician who led Lebanon after its 1975-1990 civil war.
Al-Hariri's family has called for
an international investigation
Opposition leaders and al-Hariri's supporters have blamed the Lebanese and Syrian governments for the assassination. The Lebanese and Syrian governments have denied involvement and condemned the murder.
Al-Hariri's funeral turned into a massive demonstration against Syria's presence in the country and the pro-Syrian Lebanese government.
Syria, facing mounting international pressure, said it will withdraw its troops to eastern regions close to its border.
Umar Karami, head of the Lebanese government, told Aljazeera: "The redeployment operation has been discussed since the beginning. We have always said that al-Taif accord is the basis of all these issues."
"If Syria ... is serious about withdrawing its army from Lebanon, then let it withdraw without [issuing] statements"
Faris Said, representative of Lebanese opposition
But Faris Said, a representative of the opposition, said: "If Syria ... is serious about withdrawing its army from Lebanon, then let it withdraw without [issuing] statements.
"Minister Walid al-Mualim and Umar Karami should not practise political terrorism against the Lebanese by saying the Syrian withdrawal from Lebanon will cause problems and conflicts among the Lebanese."
Meanwhile, Ghassan bin Jiddo, head of Aljazeera's Beirut bureau, reports that the meeting between Lebanese Defence Minister Abd ar-Rahim Murad and Hizb Allah Secretary-General Hasan Nasr Allah, scheduled for Friday at the headquarters of the Lebanese resistance force, has assumed special significance for a number of reasons.
Although Nasr Allah routinely meets high-level Lebanese officials, the situation after the assassination of al-Hariri is exceptional, with Syria facing mounting pressure to withdraw its troops from Lebanon in accordance with UN Resolution 1959, which also calls on Hizb Allah to disarm.