The first is October 31, the deadline imposed by the United Nations' nuclear watchdog for Tehran to prove it is not secretly developing nuclear weapons, to suspend all enrichment of uranium and to give full details of all uranium it has imported.
The International Atomic Energy Agency (IAEA) has also urged the Islamic republic to sign an additional protocol to the international nuclear Non-Proliferation Treaty (NPT) that would allow the UN's nuclear inspectors to make unannounced visits to suspected nuclear weapons facilities.
The second crunch date is November 20, when the IAEA's board of governors convenes again in Vienna to consider how to respond to the crisis.
If the IAEA governors conclude on November 20 that Iran has not answered all their concerns about its nuclear activities and is therefore in violation of the NPT, then they could refer the problem to the UN Security Council and that could lead to the imposition of international sanctions on Tehran.
"We hope that Iran gives us all the cooperation we've asked for. If they cooperate we could be able to report to our board of governors (on November that we have resolved all the outstanding issues," IAEA spokesman Mark Gwozdecky told AFP on Saturday.
"One possibility is that we conclude that their nuclear programme is solely devoted to peaceful purposes. That's what we hope for. The toughest decision that the board can take is to declare that Iran is not in compliance and to refer the matter to the Security Council.
"Between these two scenarios there are a lot of possibilities. But I don't want to speculate on those."
Iran, like Iraq and North Korea before it, is accused by Washington of illegally developing weapons of mass destruction. Tehran, which is building a civilian nuclear plant with Russian help, denies it intends to use any nuclear material for military purposes.
Pointing out that both the United States and its Middle East ally Israel have nuclear warheads, Tehran accuses Washington of double standards and of seeking to use the weapons argument as a pretext for invading the country, as it did oil-rich Iraq, in a bid "to re-engineer and re-shape the entire Middle East region".
It remains to be seen whether Iran will provide the IAEA with the cooperation it desires.
When the IAEA issued its October 31 deadline on Friday, Tehran's ambassador to the UN watchdog stormed out, accused the IAEA of pressurising it for political motives and warned that Iran could stop all cooperation with the inspectors.
Gwozdecky said he hoped the worse would not happen.
"We do not force any country to cooperate with us. We believe that Iran will understand that it is in its interest to cooperate with us because we provide a service for them.
"It's through our inspection process that they can demonstrate to the world that what they say is true. And it's only through impartial, international verification that the global community can have confidence in what is happening in Iran."
In the run up to November 20, the IAEA planned to continue its inspections in Iran, Gwozdecky said.
"We have a responsibility to do that," he explained.
"We hope that Iran will extend to our inspectors and experts their full cooperation,.. give us access to those sites which we want to visit and to answer fully all the questions we put to them," he added.
Gwozedcky said the IAEA would begin discussions with Tehran on the possibility of the Iranians signing an additional protocol to the NPT.
The IAEA would also continue to probe Iran's argument that the only reason the UN inspectors had discovered particles of highly enriched uranium at one of the sites they inspected was that it had been brought in on contaminated imported equipment.
"We will be discussing with other countries the story that Iran has imported equipment from abroad. And they have said that is why we have found particles of highly enriched uranium in our sampling," he said.
"We are waiting for Iran to give us the information but we're going to pursue this investigation."
Once the October 31 deadline arrived, the IAEA would begin preparing a new report on Iran for its 35 member nations, who would receive it by mid-November, in time for the crucial board meeting later that month, he said.