WASHINGTON - US President Barack Obama, eager to resolve at least one intractable conflict in his final two years in office, has his eye on a major prize: reconciliation with Iran.
Thursday's agreement on a road map for the final phase of negotiations on a nuclear accord could open a way to a broader realignment that would redraw the map of the Middle East.
But analysts warn that the long-time foes remain far from a rapprochement and any future co-operation would be limited.
"In Barack Obama's head, there's this fantasy of a grand bargain, an alliance with Iran, and of reconstructing the architecture of the region for a paradigm shift," said Joseph Bahout, a visiting scholar at the Carnegie Center.
"This is the fantasy of the Obama administration, but he knows it will never happen because Iran is a lot colder.
"They'll take the nuclear deal, but everything will remain business as usual," he added.
Relations between Tehran and Washington are haunted by the 1953 coup, orchestrated by the CIA, which overthrew Iranian prime minister Mohamed Mosssadegh and restored royal rule.
Shah Mohammad Reza Pahlavi was overthrown in turn in the 1979 revolution that brought Ayatollah Khomenei's Islamist and explicitly anti-American government to power.
The divide between the powers has been deepened by decades of hostile rhetoric.
The United States is regularly denounced as the "Great Satan" by Iranian leaders, and Washington has slammed Tehran as a "rogue state," part of an "axis of evil." Obama hailed the "historic understanding" with Iran Thursday, and said he is willing to engage with Iran "on the basis of mutual interests and mutual respect." But he sent Tehran a strong warning.
"This deal alone - even if fully implemented - will not end the deep divisions and mistrust between our two countries," he said.
"So make no mistake: We will remain vigilant in countering those actions and standing with our allies," Obama added, referring to what he called Iran's "sponsorship of terrorism."
The first signs of a potential thaw came in 2011, when US Secretary of State John Kerry and his Iranian counterpart Mohammad Javad Zarif met.
The closed-door encounter led to talks that have taken place over the past 18 months with Britain, China, France, Russia, the United States and Germany, known as the P5+1, to hammer out a complex comprehensive nuclear agreement.
Both sides have major stakes in seeing the deal succeed.
Removing or delaying the threat of a nuclear-armed Iran would be a stunning victory for Obama.
And for Iranians, it would spell the lifting of a rigorous global sanctions regime that has crippled the country's economy.
Obama had a historic phone call with Iranian President Hassan Rouhani in 2013, the highest-level contact between the two countries' in more than three decades.
Then last October, Obama secretly wrote to Iran's current supreme leader Ayatollah Ali Khamenei to discuss possible co-operation in the fight against jihadist militants provided a nuclear deal could be struck.
Despite these signs of outreach, restoring full diplomatic ties, severed some 35 years ago amid the 1979 storming of the US Embassy in Tehran and the painful 444-day hostage-taking, remains far off.
But that has not stopped Obama from pushing for peace with its long-time enemy.
As Iran celebrated Persian New Year last month, Obama urged leaders to seize a "historic" opportunity to begin a "brighter future," speaking in a video dubbed in Farsi.
But Obama is aware of the limits of its "high stakes investment in its Iran diplomacy," said Suzanne Maloney, senior fellow at the Brookings Institute.
"The administration has doggedly pursued a deal with Iran as the centerpiece of its Middle East strategy," she wrote on her blog for the think tank.
"Obama's outreach is not grounded an illusion of a new alliance or wholesale rapprochement with the Islamic Republic."
In March, Khamenei lashed out against "deceitful" world powers and branded a letter from Republican US lawmakers as a sign of America's internal collapse.
And the United States has long decried Iran's alliances with various countries it has blacklisted as "terrorist" nations, including Sudan, Syria and Washington's newest foe-turned-friend, Cuba.
Alireza Nader, senior international policy analyst at the RAND Corporation, is sceptical about how close Washington and Tehran will be in the future.
"I do not believe that the establishment in Iran wants normal ties with the United States," he told AFP.
"Perhaps President Rouhani and his government want diplomatic relations, but the Supreme Leader and his supporters view it as being against their interests." But that does not preclude both sides from exploring "discrete areas of co-operation" in regional conflicts.
Though a major ideological chasm separates them, overlapping concerns from Afghanistan to Syria to Iraq have forced the two to rethink the historically icy relationship.
On the margins of the sometimes laborious nuclear talks, discussions focused on the fight against Islamic State jihadists who have taken over large swathes of Iraq and Syria.
In February, Kerry said the United States and Iran have a "mutual interest, if not a cooperative effort" in defeating IS militants.
In Afghanistan too, both have a shared incentive to fight the Taliban, which poses a threat to both Iran and the United States.
Nevertheless, said Nader: "The two countries will continue to be competitors, especially if there are no major domestic changes in Iran."