Al-Hajj was tipped to take leadership of Lebanon's army if the current chief, General Michel Suleiman, who is the leading candidate for the vacant presidency, is elected to that post.
Rula Amin, Al Jazeera's correspondent in Lebanon, said that Cardinal Nasrallah Boutorus Sfeir, the Maronite Christian patriarch, set a measured tone in his address to the memorial service in Harissa.
"He tried to stay away from politics. He did say that al-Hajj was a great officer and that he tried to put as much as possible into the army," she said.
"[Sfeir] said the army is the protector of this country [but] it was interesting that the patriarch stayed away from the political manoeuvring in Lebanon," she said, adding that Sfeir was considered to be frustrated with the failure to agree on a unified political programme for the country.
Lebanon has been without a president since November 23, when Emile Lahoud stepped down at the end of his term.
The ruling March 14 majority bloc and the opposition, which is led by Shia party Hezbollah, have so far been unable to agree on a successor to Lahoud.
Suleiman has emerged as a consensus presidential candidate, but the constitution has to be amended to allow him to take office.
|Al-Hajj led operations against Fatah al-Islam |
fighters in a Palestinian camp [AFP]
Political wrangling between the majority and the opposition has held up the required constitutional amendments, meaning that parliamentary voting sessions have also been postponed.
Al-Hajj's murder has sparked warnings that Lebanon could sink deeper into its most serious crisis since the 1975-1990 civil war.
On Wednesday, security agents detained four Lebanese in whose names the car used in the bombing was registered, a security official said.
The individuals were detained near Ein el-Hilweh Palestinian refugee camp near Sidon, which is considered to be a base for radical Palestinian fighters.
Authorities are investigating if the assassination was planned by al-Qaeda-inspired fighters seeking vengeance against al-Hajj.
The commander led operations against fighters from Fatah al-Islam, which is ideologically close to al-Qaeda, hiding in a Palestinian refugee camp this year.
Fatah al-Islam was defeated by the Lebanese army after 15 weeks of fighting at the Nahr al-Bared camp, near the northern city of Tripoli.
No group or individual has claimed responsibility for al-Hajj's killing.
All schools and universities have been closed in Lebanon as part of the day of mourning.
Source: Al Jazeera and agencies