"The council of ministers has decided to instruct the prime minister to ask the UN secretary-general to provide [Lebanon] with technical assistance from the international investigation commission," the government said in a statement.
The UN is also probing the assassinations of Rafiq al-Hariri, the ex-prime minister, and seven other politicians over the past three years.
Judicial officials declined to discuss the probe into Wednesday's murder of al-Hajj, who was killed along with Khairallah Hedwan, his bodyguard, in a car bomb attack in a Beirut neighbourhood.
A police source said three Lebanese men, from the outskirts of the southern port city of Sidon, had been arrested late on Wednesday.
"They are being questioned in connection with the licence plate of a BMW car, found on the site of the blast" in Baabda, southeast of Beirut, the source said on the condition of anonymity.
Records from the motor vehicle department showed that each one of the men had owned the car at some point in the past, but that there was no clear evidence to incriminate them, the source said.
The army has said a BMW packed with explosives detonated as al-Hajj drove past. The Red Cross has confirmed eight people were wounded in the attack.
It was not clear if the licence plate found by investigators at the scene of the bombing belonged to the booby-trapped car.
No one has claimed responsibility for the killing.
Wednesday's killings have heightened tension in Lebanon where the government and opposition are struggling over resolving who should become the next president.
Al Jazeera's Zeina Khodr said: "The Lebanese are asking what will be next, what will the consequences be of the latest political assassination.
"Local observers are saying that the military as an institution was a target, perhaps a message telling the army to stay out of politics."
Al-Hajj, a 54-year-old Maronite Catholic and the military's chief of operations, was considered the leading candidate to succeed the head of the military, General Michel Suleiman, if Suleiman was elected president.Possible suspects
Lebanese army investigators are searching for clues to determine who was involved in the assassination.
Local newspapers have said that al-Hajj, killed by a 35kg car bomb, may have been the target of fighters linked to Fatah al-Islam, an armed Palestinian group thought to have links with al-Qaeda.
Al-Hajj had a leading role in the army's 15-week battle against Fatah al-Islam at the Nahr al-Bared Palestinian refugee camp in northern Lebanon this year, raising some suspicions that the group may be behind his slaying.
The As-Safir newspaper quoted a senior military source as suggesting a possible link to the group.
"We are in front of a theory that the side which committed the crime may be smaller than al-Qaeda but bigger than Fatah al-Islam," the paper quoted the source as saying.