The 77-year-old leader told a Koran reading event marking the start of Ramadan: "They [Saudi Arabia] will face certain downfall.”
Mr Khamenei also told a religious gathering: “They [Saudi leaders] act cordially towards the enemies of Islam while having the opposite behaviour towards the Muslim people of Bahrain and Yemen.”
Iran and Saudi Arabia have had an antagonistic relationship with the countries most recently having backed opposing forces in both the Yemen and Syrian conflicts.
Iran's Supreme Leader Ayatollah Ali Khamenei has issued a threat to Saudi Arabia
Relations were strained even further over US President Donald Trump visiting the Gulf state where he accused Tehran of supporting terrorism in the Middle East.
Iran has denied the accusation saying that Saudi Arabia is the real source of funding Islamist militants.
President Hassan Rouhani, who is seen as a more moderate voice in the Muslim country, earlier called for improved relations with Gulf Arab states during a telephone call with the Emir of Qatar, which has been criticised by its Gulf neighbours over its relationship with Tehran.
Islamic Revolution: Shocking moments depict the horrors of the events Fri, February 10, 2017
The event marks the 38th anniversary of the Islamic revolution, which came ten days after Ayatollah Ruhollah Khomeini's return from his exile in Paris to Iran, toppling the monarchy system and forming the Islamic republic.
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Demonstrators loot government bureaus and banks as well as liquor shops, cabarets and cinemas during the Revolution in Tehran, 4th November 1978
Mr Rouhani told Tamim bin Hamad al-Thani: ”We want the rule of moderation and rationality in the relations between countries and we believe that a political solution should be a priority.
"The countries of the region need more cooperation and consultations to resolve the crisis in the region and we are ready to cooperate in this field.”
Rouhani earlier responded to Trump's criticism by saying stability could not be achieved in the Middle East without Iran's help.
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US President Donald Trump with Saudi Arabia's King Salman bin Abdulaziz Al Saud (R)
The massive US arms deal Mr Trump signed with Saudi Arabia, to supply military arms worth £85.9 billion ($110bn), will also have undoubtedly alarmed Tehran with expectations that at least some of the military hardware and weaponry will be used against Yemen.
During Mr Trump’s speech to the Muslim world whilst in the principality he accused Iran of “fuelling sectarian violence” and called for the further isolation of the largest Shiite country in the Middle East.
Mr Trump said: "From Lebanon to Iraq and Yemen, Iran funds, arms and trains terrorists, militias and other extremist groups that spread destruction and chaos across the region.
Iran's President Hassan Rouhani
"For decades Iran has fuelled the fires of sectarian conflict and terror; it’s a government that speaks openly of mass murder, vowing the destruction of Israel, death to America, and ruin for many leaders and nations in this very room.
"Among Iran’s most tragic and destabilising interventions, you’ve seen it in Syria. Bolstered by Iran, [Bashar al] Assad has committed unspeakable crimes, and the United States has taken firm action in response to the use of banned chemical weapons by the Assad regime, launching 59 missiles at the Syrian air base from where that murderous attack originated."