Lebanon's prime minister Saad al-Hariri gestures during a press conference in parliament building at downtown Beirut, Lebanon October 9, 2017.
Hariri acknowledged in the interview that his resignation was unconventional, adding that he was ready to return to Lebanon to formally submit it and seek a settlement with Hezbollah.
It has always been a foe of Hariri but is part of the coalition government he formed previous year and called for his return.
Some Lebanese officials have said he should return with his family, so he could be free of any Saudi pressure.
Hariri's office said he met several diplomats in Riyadh on Monday including the British and German ambassadors.
El-Rai and Saudi Charge d'Affaires Walid al-Bukhari said the kingdom is not likely to deport Lebanese citizens as punishment for the participation of the militant Hezbollah group in Lebanese politics. He cited a fear of assassination and Hezbollah's "sowing strife" in the Arab world as his reasons for stepping down.
Israeli Prime Minister Benjamin Netanyahu said Hariri's resignation should serve as "a wake-up call to the worldwide community to take action against the Iranian aggression that is trying to turn Syria into a second Lebanon". Hezbollah and the Houthis deny that the Lebanese group is carrying out anti-Saudi activities in Yemen.
Hariri warned on Sunday in his first interview since resigning of possible Gulf Arab sanctions against Lebanon and of the livelihoods of the 300,000-400,000 Lebanese in the Gulf.
Hariri denied Velayati's account that the Lebanese leader had offered to mediate between Iran and Saudi Arabia.
He also repeatedly said he was ready to die for Lebanon - his father, former Prime Minister Rafik Hariri, was killed by a vehicle bomb in Beirut in 2005 - but added that he didn't want his children to go through that kind of ordeal.
Maronites number about 900,000 in Lebanon, around a quarter of the population.
Lebanese politicians have previously held talks on Hezbollah's arsenal as part of a dialogue on a national defence strategy, but have never seriously discussed disarming it.
Echoing Saudi demands, MPs from Hariri's Future Movement called for a United Nations resolution from 2006 that demanded all militias in Lebanon disarm to be respected.
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