Al-Hariri, Beirut's most prominent Sunni politician, was initially nominated prime minister after the June elections, but stepped down after more than 10 weeks trying to forge a unity government including Hezbollah and its allies.
Rival political factions have traded accusations of blame since the failure of the talks.
Instability and violence
But there has been no sign of compromise over the differences that derailed al-Hariri's first attempt, chief among them his refusal to accept the conditions of Christian politician Michel Aoun, an ally of the Shia group Hezbollah.
The parliamentary bloc of Shia parliament speaker Nabih Berri, who nominated al-Hariri for prime minister in June, did not nominate anyone for the post on Tuesday.
Likewise, MPs belonging to Aoun's bloc and Hezbollah did not nominate anyone.
Politicians say the deadlock reflects a relapse in ties between Saudi Arabia and Syria, states with great influence in Lebanon and whose rivalries have fuelled political instability and violence in the country over the past four years.
Rapprochement between Damascus and Riyadh this year has helped Lebanon enjoy its longest spell of political stability since the 2005 assassination of former prime minister Rafiq al-Hariri, Saad's father.
However, the postponement of a visit Saudi's King Abdullah was due to make to Damascus has signalled a freeze in the improvement.
Many Lebanese fear that could be reflected in a protracted political standoff over the new government.