Many observers expect the four-stage polls to sweep the anti-Syrian opposition to power, even though the main alliance has splintered.
The elections will be held on three consecutive Sundays to fill all 128 seats in the legislature.
Saad, son of slain former prime minister Rafik al-Hariri and a Sunni Muslim, plans to travel to the north and the east, where there is a sizable Sunni population, to join allies in trying to forge tickets and negotiate coalitions that could win the opposition more seats.
On Monday he stressed his alliance with Druze leader Walid Jumblatt and Christian factions who "stood by us".
Speaking on his Future Television, Saad promised "to continue our alliances all over Lebanon ... and we are with them all the way".
Saad's bloc is expected to
sweep the four-stage polls
His Sunni and Christian allies in the north face pro-Syrian Christians and Muslims and one-time opposition members who have decided to go it alone or are considering joint runs with pro-Syrians.
In the eastern Bekaa Valley, Hizb Allah and Amal are also expected to dominate the heavily Shia-dominated Baalbek-Hermel constituency.
So the opposition battle is in the western Bekaa and central constituencies.
Reflecting Lebanon's bizarre political alliances, Michel Aoun, a staunch anti-Syrian former army commander who broke with Saad and Jumblatt, is running in the Christian heartland of Kesrwan-Byblos district against one-time allies and is challenging Jumblatt's dominance in the Baabda-Aley mountain region overlooking Beirut.
There, Aoun's candidates are allied with Talal Arsalan, a pro-Syrian Druze rival of Jumblatt, while Jumblatt and Saad candidates are running together with Hizb Allah.
Christian leader Michel Aoun is
contesting against former allies
Aoun, who returned from 14 years' exile on 7 May, is expected to field candidates in the north and the east.
Saad said he was surprised by the "strange" alliances Aoun was forging.
President Emile Lahoud has blamed Lebanon's electoral law for the low turnout in parliamentary polls in Beirut, but chose to remain silent on Saad al-Hariri bloc's victory.
The pro-Syrian Lahoud, whose political survival may be at stake after the 29 May-19 June elections, said on Monday that the turnout in Beirut, the first region to vote, "proves our theory that the present electoral law does not meet aspirations of the Lebanese people".