WASHINGTON — After Iran and the major powers signed on to an interim deal on Tehran’s nuclear program, expectations were high. Over the last week, they have fallen sharply as Iranian officials have made tough public comments, Israel’s prime minister has reaffirmed his opposition to almost any conceivable deal, and several influential U.S. senators have threatened to enact new sanctions. This does not mean a final deal with Tehran is impossible, but it does mean that both sides, Tehran and the West, need to start thinking creatively about how to bridge what is clearly a wide divide and how to get around the main obstacle they will face — which is not abroad but at home.

The Iranian statements that have attracted so much attention came from both the foreign minister and president. The former, Javad Zarif, explained to CNN’s Jim Sciutto that, contrary to what Washington had repeatedly claimed, Iran “did not agree to dismantle anything.” Later, in an interview with me also on CNN, President Hassan Rouhani explained that Iran would not destroy any of its existing centrifuges. He also indicated to me that Iran would not shut down its heavy-water reactor at Arak, a point of contention with the West, which worries the facility can produce plutonium that could be used to make a bomb.

Iran and America have fundamentally different views about an acceptable final deal. On the basis on my interview with Rouhani and talks with other Iranian officials, my sense is that the Iranian vision is as follows. Iran will provide the world with assurances and evidence that its nuclear program is civilian, not military. This means that the country would allow unprecedented levels of intrusive inspections at all facilities. This process has already begun. The interim agreement calls for international inspections at Iran’s centrifuge production factories, mines and mills. This week, for the first time in a decade, inspectors have entered Iranian mines.

But Iran’s officials are determined not to accept any constraints on their program. They speak often about the importance of being treated like any other country that has signed the nuclear Non-Proliferation Treaty, which to them means having the unfettered right to enrich uranium to produce electricity. In fact, the NPT says nothing about enrichment activities specifically. Many countries with nuclear power plants do not enrich but others do, which allows Iran to claim, reasonably, that enrichment has so far been a permitted activity. The only criterion that the treaty lays out is that all nuclear production must be “for peaceful purposes.”

The American vision of the final deal is quite different and stems from the notion that Iran must take special steps to provide confidence that its program is peaceful. It would allow Iran to enrich some small, symbolic amount of uranium, up to a 5 percent level (which makes it time-consuming to convert it to weapons-grade levels). Beyond that, Tehran would dismantle thousands of its existing centrifuges and shut down its heavy-water reactor. Washington wants to lengthen the lead time between a civilian and military program.

Both sides will have to think hard about their core concerns. Iran’s officials will have to come to terms with the fact that their country is being treated differently and for good reasons. Iran has a program that is suspicious — a massive investment to produce a tiny amount of electricity — and the country has deceived the world about its program in the past. Washington will have to recognize that while it will get more concessions than it thought possible on inspections, it will get fewer on the rollback of Iran’s existing program. If it can ensure that it has a real lead time — six to nine months — that’s a significant achievement. After all, if Tehran throws the inspectors out, that would change the situation instantly — and Washington would not need six months to react.

There are creative compromises that can bridge many of the gaps. Georgetown University’s Colin Kahl and Joseph Cirincione, who both work on these issues, pointed out to me that one could shut down centrifuges without destroying them. In fact, Iran has more than 19,800 installed centrifuges, but fewer than half are operational. Such compromises have already been found.

Iran had always said it would not ship away its store of 20 percent enriched uranium, but in the interim agreement, it agreed to neutralize it by dilution and oxidation. Similarly, Iran could keep its heavy-water reactor running but convert it to a light-water system.

I have come away from meetings with Rouhani and Zarif convinced that they are moderates who seek greater integration of Iran with the world. (Rouhani hinted to me, for example, that in the next few months, the leaders of the Green Movement would be released.) But I am also sure that they are operating under constraints, with many domestic opponents. The same could be said of the Obama administration. It is better that both sides start preparing the ground domestically for a final deal — and the compromises it would involve — rather than hoping that somehow if it works out in Geneva, it will work out at home as well.

Fareed Zakaria is a columnist with the Washington Post Writers Group.