Story highlights U.S. President Barack Obama was meeting Israeli PM Benjamin Netanyahu Monday

Amanpour: Obama will again urge Israeli restraint on military action against Iran

White House knows that Iran will not give up its right to enriching uranium, she adds

Can Obama convince Netanyahu there is still time and space for diplomacy to work

What is at stake in the meeting between the leaders of the United States and Israel?

U.S. President Barack Obama was meeting Israeli Prime Minister Benjamin Netanyahu on Monday, in what could be one of the most difficult yet significant encounters with a foreign leader since his inauguration. Nothing less than another war in the Middle East is at stake, and administration officials tell me Obama will again try to urge Israeli patience and restraint when it comes to military action over Iran's nuclear program. He previewed his stance when he spoke at the annual American Israel Public Affairs Committee conference in Washington D.C. on Sunday, making his own tough stance against Iran's nuclear program clear and insisting that he "[has] Israel's back."

"I have said that when it comes to preventing Iran from obtaining a nuclear weapon, I will take no options off the table, and I mean what I say," Obama said.

What do the Israelis want from the U.S.?

Speaking to AIPAC later the same day Israeli President Shimon Peres, a veteran of three decades of peace negotiations with the U.S., told the crowd Israel could not have a better friend than Obama. Peres said: "The most important issue for Israel is our security. I think under President Obama we have the best relationship on the issue of security. Never were the security ... needs better met than today under President Obama."

And later the more hawkish Netanyahu issued this statement: "I very much appreciated the fact that President Obama reiterated his position that Iran must not be allowed to develop nuclear weapons and that all options are on the table. I also appreciated the fact that he made clear that when it comes to a nuclear-armed Iran, containment is simply not an option, and equally in my judgment, perhaps most important of all, I appreciated the fact that he said that Israel must be able to defend itself, by itself, against any threat. I appreciate all his statements, and I look forward to discussing them further with President Obama tomorrow."

But earlier on a trip to Canada, Netanyahu had made these demands on Iran. "Dismantle the underground nuclear facility in Qom, stop enrichment inside Iran and get all the enriched material out of Iran. And when I say 'all the material,' I mean all the material."

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How likely is Iran to bow to pressure?

The White House knows that Iran will not give up its right to enriching uranium, and therefore Netanyahu's demands are a non-starter, U.S., European and Arab officials tell me.

The key for nuclear negotiations between Iran and the group of countries known as P5+1 (the United States, the United Kingdom, France, Germany, Russia and China) is not uranium enrichment per se, but the level of enrichment and Iran's intentions.

To this end, and with new nuclear negotiations back on the table, diplomats and experts I have spoken to are now saying there could be a new starting point for those talks. Iran's supreme leader, Ayatollah Ali Khamenei, issued a fatwa years ago, decreeing that the production, possession, use or threat of use of nuclear weapons is "a Great Sin." He repeated it publicly last month, and just in case anyone missed it, Iran's foreign minister and former head of Atomic Energy Agency, Ali Akbar Salehi, repeated the fatwa last week. Islamic scholars explain that when Shiite leaders issue fatwas, it is akin to "religious law." Since Iran has also asked to start up nuclear negotiations again, some officials are now saying, the P5+1 should take Ayatollah Ali Khamenei at his fatwa and verifiably take weaponization off the table.

What is Obama's challenge?

Iran insists on the right to enrich uranium for civilian purposes under the Nuclear Non-Proliferation Treaty and wants explicit formal acceptance of such; hence its pursuit of a nuclear program despite foreign sanctions.

If negotiations with Iran re-start, the Obama administration will be faced with the crucial question of whether it can pursue real diplomacy, which includes incentives and disincentives, despite Iran grandstanding, haranguing and being difficult negotiators. This is not at all certain in an election year. Yet given President Obama's strong preference for a permanent negotiated solution to Iran's nuclear program, which he reiterated Monday at the AIPAC conference, that is what it will take.

His challenge will be to convince the Israeli prime minister in private what he says publicly: Namely he believes there is still time and space for diplomacy to work.