Renewed efforts to take the heat out of the dangerously escalating Iran nuclear crisis face a stern test this week with two crunch meetings, first in Tehran on Monday and then in Baghdad two days later.

In Tehran, International Atomic Energy Agency (IAEA) head Yukiya Amano, in his first visit as director general, will press Iran for closer cooperation in order to relieve its long-held suspicions of a covert nuclear weapons programme.

But a perhaps more important gathering comes on Wednesday in Baghdad when Iranian officials meet counterparts from the P5+1 world powers -- Britain, China, France, Russia, the United States, and Germany -- plus the European Union.

Both events follow earlier rounds, in the IAEA's case last week and for the P5+1 in Istanbul last month, that found enough common ground and willingness to engage to at least meet again.

But on both tracks, negotiators now face much more of a challenge as they tackle the thorny issues that have divided not only Iran and much of the international community, but also the P5+1 powers themselves, for years.

They also represent another try at finding a diplomatic solution to a crisis that has escalated since Barack Obama offered Tehran an "extended hand" if it "unclenched its fist" on becoming US president in January 2009.

Since then Iran has significantly ramped up its nuclear programme, leading to increased sanctions -- including on its lifeblood oil sector -- because of fears that its activities are not, as Tehran insists, purely peaceful.

Most notably, Iran is now enriching uranium to purities of 20 percent, a significant jump towards 90-percent weapons grade and shortening the "breakout" time needed to create a bomb -- if it decided to do so.

Israel has meanwhile strongly hinted that it could launch military strikes on Iran if diplomacy fails. Obama criticised in March "loose talk of war" but also said he would "not hesitate to use force when it is necessary".

Israeli Prime Minister Benjamin Netanyahu warned on Friday that Tehran could use the upcoming talks "to delay and deceive and buy time".

Iran, which has seen several nuclear scientists assassinated in attacks it blames on Israel, has threatened to block the Strait of Hormuz and has conducted military manoeuvres including sending warships through the Suez Canal.

In October 2009, P5+1 talks with Iran in Geneva promised much but delivered nothing, with mooted fuel swap deals foundering and negotiations with world powers collapsing in Istanbul in January 2011.

Earlier this year, after two visits to Tehran the IAEA broke off talks, saying that Iran was refusing to address suspicions of weapons research outlined in a key November report and to allow it access to the Parchin military site.

But now both sides have shown a willingness to give diplomacy another try.

"In a way both sides have walked up to the abyss and they have both decided they don't want to go down it," Trita Parsi, author of a new book about Obama and Iran called "A Single Roll of the Dice", told AFP.

Iran "has its back against the wall", said one Western diplomat.

Tehran wants international acceptance of its right to peaceful nuclear activities, for sanctions to be lifted and for the threat of military action to disappear. It also wants to be reassured the West is not seeking regime change.

The P5+1 will want Iran to take a series of steps that convince it once and for all that the real aim of Tehran's nuclear activities are peaceful, including through closer cooperation with the IAEA.

Neither meeting is expected to produce spectacular results, however, with diplomats saying the most likely outcome will be both sides setting the parameters for a lengthy process of compromises and give-and-take.

Even if Iran offers to suspend 20-percent enrichment or turn off the centrifuges at its Fordo site under a mountain near Qom, it will be disappointed if it expects to be offered sanctions relief in return, analysts said.

"The results might not be that tangible," one P5+1 diplomat told AFP, playing down expectations for a meeting that he nevertheless said was highly important.

"A positive outcome from Baghdad for us would be to come out and realise that we had a serious discussion with the Iranians on concrete aspects of their programme and that they engaged in dialogue."