Since taking office last month, Iranian President Hasan Rouhani has signaled his country could be more conciliatory about international fears his country is seeking nuclear arms — something Tehran denies.

Progress on the issue remains difficult after more than a decade of growing nuclear tensions because of the wide gap between what Iran seeks from the West and what it is willing to concede as the first steps of any negotiated deal.

With Rouhani and President Barack Obama both scheduled to address the U.N. General Assembly on Tuesday, here is a look at who wants what, and what each may be willing to give in return:

WHAT IS THE SITUATION?

Iran has ruled out any chance of closing down its uranium enrichment program, which the West fears could eventually produce material for nuclear weapons. Iran insists it only seeks reactors for energy, research and isotopes for medical treatments.

The two sides have been in a virtual stalemate over the issue since international talks began in 2006 with each side blaming the other for intransigence. The U.S., EU, U.N. and other countries and groups have applied painful sanctions on Iran, leaving the country blocked from global banking systems and with sky high inflation.

WHO ARE THE PLAYERS?

The U.S. is negotiating with Iran alongside, Russia, China, Britain, France and Germany. Except for Germany, all these nations are permanent U.N. Security Council members, and the group is called the P5 + 1

Israel has no diplomatic ties with Iran and is not part of negotiations over Tehran's nuclear program. But it's involved because it considers an Iran armed with nuclear weapons an existential threat and has threatened possible military attack.

While the P5 +1 aims at a picture of unity, there have been some differences on tactics, with Russia and China sometimes pushing through negotiating demands more favorable to Iran.

WHAT'S HAPPENING AT THE U.N. GENERAL ASSEMBLY?

The broad challenges posed by sanctions will shape Rouhani's agenda at the meetings. Obama is expected to signal his willingness to engage with Tehran if it makes nuclear concessions.

Obama's speech will be closely watched for signs that he may meet later in the day with Rouhani. Even a brief encounter would be significant given that the leaders of the U.S. and Iran haven't had face-to-face contact in more than 30 years.

But the meeting is unlikely to result in either side offering concessions on the nuclear issue.

WHAT DOES IRAN WANT?

Iran wants swift relief from international sanctions led by the U.S. and European Union targeting its vital oil exports and limiting its access to global financial networks. Sanctions have been progressively imposed since 2006 in attempts to force it to compromise on its nuclear program.

Iran may be ready to agree to limit enrichment to no higher than 5 percent and destroy or convert all enriched uranium above that benchmark as an initial concession. It now is enriching some uranium to nearly 20 percent, which can be turned into weapons-grade uranium much more quickly.

Iran sees Israel's undeclared nuclear arsenal as the biggest threat to the Middle East.

WHAT DOES THE U.S. WANT?

Since the start of international talks on Iran's nuclear program seven years ago, the United States and its allies have moved from demanding a full stop to all enrichment activities to seeking lesser concessions from Iran.

The P5 + 1 group wants Tehran to stop enrichment above 5 percent as an initial step. It also seeks an end to work on a reactor that will produce plutonium because that material can also be used to arm nuclear weapons. It wants a fortified underground facility shut down the U.N. nuclear agency to have greater powers in monitoring Iran's nuclear program.

As a first step, the six-nation group is likely to welcome an agreement to either stop enriching above 5 percent or cease work on the reactor. Tehran is unlikely for now to offer to shut down the underground enrichment plant where it now makes 20-percent enriched uranium.

Washington faces a policymaking quandary since many believe sanctions may have forced Iran into a bargaining mood. However, some sanctions relief may be offered in return.

AND ISRAEL?

Israel wants the U.S. and the broader international community to maintain a "credible" military threat and has rejected the more moderate tone of the Rouhani administration as a smoke screen.

Prime Minister Benjamin Netanyahu is concerned that its allies might be fooled into complacency. In a statement last week, he demanded Iran halt all uranium enrichment; remove all enriched uranium from its territory; close the underground facility where 20 percent uranium is being made, and end construction of the plutonium reactor.

Even if Tehran concedes on only one of the demands as an initial step, Netanyahu's position — and indirect influence on the United States' negotiating stance — would be weakened.