Both sides in the Iran nuclear crisis are in a better mood for compromise than at any other time in the Obama presidency, having stared into the "abyss" of potential conflict -- and stepped back.

This at least is the view of Trita Parsi, author of an acclaimed recent book about the US president's doomed early attempts to reach a deal with the Islamic republic called "A Single Roll of the Dice."

"Both sides have walked up to the abyss and they have both decided they don't want to go down it," Parsi told AFP in an interview ahead of Wednesday's crunch meeting in Baghdad between Iran and six world powers.

"The opportunity has suddenly emerged in a way that wasn't there before."

Shortly after becoming president, Barack Obama offered a radical change in approach to his predecessor George W. Bush in dealings with Iran, famously offering an "extended hand" to Tehran if it "unclenched its fist."

This failed, Parsi says, not only due to "tremendous tensions" in Iran in the violent aftermath of 2009's rigged elections and some US inflexibility, but also because of mutual mistrust and insufficient political will on either side.

In the meantime the stakes have risen.

Iran has ramped up its nuclear work, stoking fears it is bent on getting the bomb, which it denies. As a result it has been hit by more painful sanctions, and what Obama called the "drums of war" have been beating ever louder.

Now though, Tehran has dropped its precondition not to broach the nuclear issue before sanctions are lifted.

Washington, meanwhile, "has made it quite clear," Parsi believes, that it is prepared to drop its long-held objection to Iran enriching uranium -- which can be used for peaceful purposes but also for a bomb -- if it cooperates.

"That was a big breakthrough because it was a big block in the past because the Iranians were very reluctant to go into the negotiations if the purpose was to do away with something the Iranians view as their right," Parsi said.

Israel, which sees itself as Iran's number one target if Tehran gets the bomb, has made it clear retreating from "zero enrichment" crosses a red line. But Parsi believes even they might come round.

"Once we reach a situation in which the Israelis realise the negotiation process is sufficiently robust and it can't be changed, then I think we are going to see a change in the Israeli posture," Parsi said.

Concessions that the P5+1 -- the US, Russia, China, France and Britain plus Germany -- would like Iran to make include suspending enrichment to purities of 20 percent, and agreeing to give the UN atomic agency more access to sites.

But even if Iran agreed to these -- which may not be in Baghdad but later, if it all -- they will be disappointed if they expect sanctions to be lifted in return, Parsi said.

"The difficulty, legally and procedurally, of lifting sanctions is actually to the detriment of the West right now," he said, depriving the P5+1 of a useful "bargaining chip."

"It's not going to be a reciprocal process if the Iranian concessions come at the front end, and the American concessions come at the back end, several years later," he said.

"That is simply not going to fly."