These statements may have been prompted by remarks made the previous day by the French ambassador to the United Nations. Speaking at an event hosted by the Atlantic Council, Gerard Araud said that it now seems very unlikely that the nuclear negotiations will reach a conclusion by their deadline, or even soon after.

The trouble stems from persistent difficulties in reconciling the positions of the Iranians and the Western powers, especially as Tehran continues to introduce new constraints and dispute American statements regarding what was in the framework agreement supposedly reached on April 2.

In the past two weeks, Iranian Supreme Leader Ali Khamenei and several leading Iranian military officers have declared that inspections of military sites will not be permitted under any deal. This is a provision that both the French negotiators and the International Atomic Energy Agency have described as unacceptable.

The demand for such inspections was presumably being alluded to on Thursday when Iranian Foreign Minister Mohammad Javad Zarif suggested that the positions of some negotiating parties are grounded “in illusions” and that “excessive demands” on the part of the Western powers would make it difficult for the talks to reach a successful conclusion by the end of June.

But critics of the Iranian regime have regularly claimed that it is the Iranians who are making excessive demands in this process. The obstruction of military sites would seriously diminish confidence in any verification methods that are built into the agreement. Nonetheless, Tehran refuses to concede to sanctions relief that is phased-in as the regime’s compliance is demonstrated. Instead, Zarif has declared that the regime will not accept any agreement that retains economic pressure beyond the date of signing.

By adding demands for constrained inspections to demands for immediate sanctions relief, Iran has arguably justified criticisms of the nuclear talks for accommodating too many of Iran’s demands. In an online talk in May, former US Special Envoy for Nuclear Nonproliferation Robert Joseph said that the Obama administration has conceded to each new demand made by the Iranian regime, thus prompting the regime to add additional demands on top of them.

Joseph added that the main obstacle to an agreement is whether the regime can “take yes for an answer.” But its rising demands are also generating more push-back from less conciliator players in the negotiating process. The comparatively hawkish US Congress has passed legislation guaranteeing oversight of the deal, meaning that if Obama concedes to limitations on nuclear inspections, the agreement may face serious difficulty in being implemented by the US government.

The possibility also exists for such a conciliatory agreement to be obstructed by the European members of the P5+1. The New York Times reported on Thursday that in addition to raising doubts about the timeline of the negotiations, French diplomats have plainly stated that they will not sign an agreement that does not include inspections of military sites.

Discord over this and related issues may not only delay an agreement; they may prevent it altogether. Xinhua News Agency reported on Wednesday that US officials have contradicted Abbas Araqchi’s claim about the possible continuation of the talks long beyond their deadline. The US is reportedly not considering any further extension of the talks. Thus, if French diplomats are correct about an agreement not being reachable by June 30 or soon after, the consequence may be the ultimate collapse of the negotiating process.