Official results are expected to be announced by Interior Minister Nouhad Machnouk later on Monday, although no time has been set.
The prime minister admitted that he had hoped for a stronger showing but said he remained happy with the result, which contrasts with the expected gains made by the rival camp led by the Shiite group Hezbollah.
"We were betting on a better result", the premier said.
Hezbollah's simple majority bloc will allow them to veto any laws they oppose, but it would take a two-thirds majority to pass big legislation, such as amending the constitution.
"Hariri's loss will be the distinguishing mark of these elections, which will have consequences on the battle to form a new government", the pro-Hezbollah Al-Akhbar daily wrote earlier on Monday. The United States designates Hezbollah as a terrorist group and also arms and trains the Lebanese army.
Iran's Foreign Ministry spokesman lauded the exemplary democratic process in Lebanon, saying Tehran respects the vote of Lebanese people and will support any government that the Arab country's new parliament elects. Economic stagnation and the general disappointment over the devastating war in neighbouring Syria leading to a massive influx of refugees into Lebanon might have propelled them against the prime minister, the AP report said.
In line with the "national pact" dating from independence in 1943, the president must be a Maronite Christian, the prime minister a Sunni Muslim and the parliament speaker a Shiite.
Hariri, and other senior politicians, blamed the unexpectedly weak turnout on a new electoral law which appears to have confused or disappointed voters.
On Sunday, Lebanese people voted for their favorite candidates competing for 128 parliamentary seats.
The Christian and heavily anti-Hezbollah party Lebanese Forces seemed to have doubled their numbers, growing from 8 to 15 seats this election.