Kuwait became the sixth state after Saudi Arabia, Bahrain, the United Arab Emirates, Sudan and Somalia to cut or downgrade diplomatic ties with Tehran.
As the tension rises, Syrian opposition groups are meeting in the Saudi capital Riyadh to try to find common ground for a peace agreement.
But both Iran and its allies are excluded.
Meanwhile, Syrian government troops are making progress on the ground, pushing the Islamic State armed group onto the defensive after increased involvement by Russia and Iran on the ground.
The rift between Saudi Arabia and Iran "makes it much more difficult to negotiate any kind of agreement between Saudi Arabia, Iran and Turkey,” says Firas Abi Ali, a senior analyst with HIS Country Risk in London.
“The accusations by both states that the other side is a sponsor of terrorism or that it is acting irresponsibly in the region and this kind of very public criticism makes it harder to be seen to compromise with your rivals,” he told RFI.
Riyad and Tehran are widely accused of fighting a proxy war in Yemen and there are fears that it may now greatly intensify as a result of the war of words between them.
The war in Yemen, which is Saudi Arabia’s southern neighbor, made the ruling family in Riyadh particulary nervous.
“The Saudis ended up being surprised by the extent of progress that the [Iranian-backed] Houthi and [former president Ali Abdallah] Saleh were making," says Abi Ali.
“They intervened not because of a change in policy but really because of a lack of other options. Had they not intervened when they did, the Houthi and Saleh would have been in control of both Aden and Sana'a. They would be able to say that they represent Yemen and that would be an outcome that was not acceptable to the Saudis."
Saudi Arabia entered the Yemeni conflict without a real plan on how to pursue it or how to exit, he argues.
Meanwhile, the Gulf state and Saudi ally Qatar has not yet downgraded its diplomatic relations with Iran.
“Doha is taking a wait-and-see attitude,” says Mahjoub Zweiri, a political scientist at Qatar University.
But the rift will not affect the current peace process too much, he says, “because the problem with Syria is not Iran but Russia. Russia is one of the permanent members of the [UN] Security Council, with a veto right. Iran is just another player.
“Iran is actually determined to delay a solution. They may affect it, they may have a bad influence but they are not really the only player. Russia is the main player. I think there is an attempt from Turkey, and from Saudi Arabia, to move ahead on the plan so they can have a unified political body that can represent Syria and then they move on to the second phase.”
But the aggravated Saudi-Iran rift may be a gamechanger.
“The latest developments will strengthen the positions of Saudi Arabia on the negotiating table about Syria,” says Guenter Meyer, a Middle East watcher at Germany's University of Mainz.
“The plan of the UN is excellent but, if we look at the different political intentions of Saudi Arabia, of Qatar, of Turkey, the regional powers all have different aims and certainly will not accept that [Syrian President] Bashar al-Assad at the end will come out as a winner.”