Rai also held talks with Hariri, who stepped down during a televised address on November 4 from Riyadh, in which he accused Hezbollah, the powerful Shiite movement that is part of his government but also close to Iran, of controlling Lebanon.
Iran said on Monday that it does not interfere in Lebanon and that comments on Sunday by Saad al-Hariri, who resigned as Lebanese prime minister nine days ago, gave hope he would soon return to his country, state TV reported.
His resignation came as tensions rise between Riyadh and Teheran, which back opposing sides in power struggles from Lebanon and Syria to Yemen.
Writing on Twitter, Hariri urged Lebanese to remain calm, adding that his family would "stay in its country, the Kingdom of Saudi Arabia", he said.
France joined Germany yesterday in calling for an end to external interference in Lebanon - buffeted for decades by conflicts between bigger players in the region such as Iran and Syria.
On Thursday, he will visit the Saudi capital Riyadh.
Foreign Minister Gibran Bassil's first stop on Tuesday was in Brussels, followed by Paris.
Amid "the state of deadlock" in Lebanon following the resignation of its prime minister, the prelates said they were concerned that he has not yet returned to Lebanon, stressing that this is "necessary for the sake of dignity, sovereignty and stability".
French President Emmanuel Macron spoke by phone on Sunday with UN Secretary-General Antonio Guterres and the two leaders agreed to take stock on Wednesday on the sidelines of the COP23 climate conference in Bonn.
"In order to prevent this we need especially the return of the current prime minister, reconciliation in the country and the prevention of influence from outside", he said.
Hariri abruptly announced his resignation in a television broadcast, saying he believed there was an assassination plot against him and accusing Saudi Arabia's arch-foe Iran and its Lebanese ally Hezbollah of sowing strife in the Arab world. The visit aims to rally diplomatic support and explain Lebanon's predicament following Hariri's move.