Oil Price | Tsvetana Paraskova: For nearly a week, the oil market has been digesting reports that Saudi Arabia and Russia are considering bringing back some production to �ease market and consumer anxiety� over high oil prices.

Accordingly, oil prices plunged, while market participants and analysts are trying to quantify how much oil supply OPEC and its allies could or would bring back online.

The Iran issue and the return of U.S. sanctions�the key driver of the oil price rally that drove Brent to $80 per barrel earlier this month�seem to have taken a backseat in investors� minds.

Yet, the consequences of the U.S. withdrawal from the Iran nuclear deal, the possible Iranian response, and the actual physical barrels of oil that could be taken off the market are still very much an important�and no doubt bullish�factor for oil prices.

One of the most drastic reactions from Iran could be Tehran pulling out of the 1968�Treatyon the Non-Proliferation of Nuclear Weapons (NPT)�a treaty in which�93 countries, including Iran, have vowed never to obtain nuclear weapons.

Last month, as well as last week, senior Iranian officials said that exiting the NPT �is one of the options on the table.�

�I think this is the question the market is ignoring right now. I would watch very closely the Iranian announcement to pull out of the nonproliferation treaty,� Helima Croft, global head of commodity strategy at RBC Capital Markets, told�CNBC�on Tuesday.

�If they pull out of the NPT, that would signal that not only are the Iranians going to resume their program, they�re resuming it with a military option.�

�And then it would become, I think, an arms race in the Middle East,� Croft said.

Two weeks before the U.S. withdrawal from the Joint Comprehensive Plan of Action (JCPOA), commonly known as the Iran nuclear deal, a senior Iranian official said that Tehran�might withdraw�from that separate 50-year-old global treaty, if President Trump pulled out of the JCPOA.

At the end of last week, while Iran was meeting with the other signatories to the JCPOA, a senior Iranian official told the�Financial Times�that Iran could exit the NPT if hardliners in Tehran prevail.

While the easiest option for Iran would be to just also pull out of the JCPOA and return to the situation before the 2015 deal, �The other solution that some actually promote is for Iran to go out of the NPT, or at least reconsider and revisit our nuclear doctrine,� the official told FT.

Before last Friday�s meeting, Iran�s Supreme Leader Ayatollah Khamenei had�issued five demands�to the European Union (EU)�including Europe guaranteeing Iran�s oil will be completely sold�as the European bloc is trying to salvage the deal.

After the meeting, a senior EU official told FT:

�We were very clear we can�t give guarantees but we can create the necessary conditions for the Iranians to keep benefiting from the sanctions lifting.�

Participants in the meeting �discussed common efforts with a view to practical solutions concerning the following issues within the next few weeks: maintaining and deepening economic relations with Iran; the continued sale of Iran�s oil and gas condensate petroleum products and petrochemicals and related transfers; effective banking transactions with Iran,� the EU�said�after the meeting.

According to John Kilduff, founding partner at energy hedge fund Again Capital, who spoke to CNBC:

�And as much as European Union officials are trying to say that they want to have a workaround against these U.S. sanctions, all the companies, the banks and the oil companies, are all in the process of pulling out and saying we�re not touching that with a 10-foot pole.�

Commenting on the possible Iranian response, RBC�s Croft told CNBC:

�If they come to believe that the U.S. and the regional partners are pursuing regime change, I think we could get a very nasty Iranian response.

According to Croft and Kilduff, the U.S. withdrawal from the Iran nuclear deal is putting Saudi Arabia firmly back in control of the oil market.

�If there�s one thing this episode should tell us all, we are not the swing producer. Saudi Arabia is,� Kilduff told CNBC. �They�re more in control now than I�ve ever seen.�

The U.S. exiting the Iran deal was something Saudi Arabia very much wanted, and �We�re back hat in hand to the Saudis saying put more barrels on the market,� Croft said.

The strategist doesn�t believe that the OPEC/non-OPEC allies would put as much as 1 million bpd back on the market, because the Saudis have their own revenue needs. But Saudi Arabia could replace some of the Iranian oil barrels that the U.S. sanctions could potentially stifle.

�The Saudis are going to help put the screws to the Iranians and again, I�m just not sure that the Iranians are going to sit back and take it so well.�