War weariness should never be written off as a reason for conflicts grinding to a halt.

That could be the case in Syria where, for the first time, government sources have conceded that their army is unable to inflict a decisive defeat on the opposition forces and is only capable of holding the ground.

If that is the case - and deputy prime minister Qadri Jamil seemed pretty confident when he made the claim on Friday - then it follows that the rebel Free Syrian Army must also be in a similar state of paralysis.

Their cause has not been helped by the US decision to withhold air strikes after last week's compromise deal which has seen Syria complying with the demands to hand over its chemical arsenal.

So is peace breaking out all over the Middle East? Not exactly, but with the UN General Assembly due to open this week there is a narrow window of opportunity to put further pressure on the government of President Bashar al-Assad to scale back its military operations and perhaps even agree to a general ceasefire.

That same opportunity could also see the first steps to engineering a deal between the US and Iran, which have been at loggerheads since the Islamic Revolution of the late 1970s.

On the face of it there is no reason why the two countries should see sense. Iran has been Assad's main regional supporter and, despite UN sanctions, still shows no sign of giving up its nuclear ambitions. With its support for Hezbollah and its strident anti-Semitism it has also been a pain in the neck to Israel, Washington's main ally in the Middle East.

Yet even in this most intractable and long-lasting of confrontations there has been an eruption of war weariness. Partly it has come from the parlous state of the economy and the realisation that sanctions have been biting.

Partly it comes from the recent election of the moderate Hassan Rouhani as president, but the main reason seems to be that the Iranian leadership is prepared to gamble on an otherwise unremarkable communication from President Barack Obama in which he proffered the hand of friendship to Rouhani on condition that he agrees to "cooperate with the international community, keep your commitments and remove ambiguities".

The speed with which this has been accepted by the Iranians suggests to US diplomats that there could be a breakthrough when the two men meet later this week at the opening of the UN General Assembly in New York.

Taking a leaf out of the approach taken by Russia's President Putin who outlined his Syrian proposals in an article in the New York Times, Rouhani used the Washington Post to urge western leaders "to make the most of the mandate for prudent engagement that my people have given me and to respond genuinely to my government's efforts to engage in constructive dialogue."

In other words here is a once-in-a-lifetime opportunity for Obama to seize the offer of Rouhani's willingness to negotiate, to end the long-running and increasingly dangerous stand-off and to bring Iran in from the cold.

If that sounds too good to be true, it has to be balanced by an understanding that Rouhani can only make this offer once. Since being elected in June he has benefited from the fact that Iran's hard-line clerics and army commanders have been sidelined - but only for the time being.

This gives Rouhani the opportunity to enter into negotiations with Obama, but he will have to get a result if he wants to remain in power. That would entail a US agreement to ease sanctions in return for an Iranian undertaking to be more transparent in its nuclear dealings.

Given the history of mutual suspicion which has underpinned the relationship between the two countries it is a big risk for both parties, but the reality is that Rouhani has the most to lose.

He knows that his country's economy is being kept in the doldrums by sanctions, and wants to use his nuclear technology as a bargaining chip. Win and he wins everything; lose and he loses all.

One thing is certain: something will have to give or the stalemate will continue and Rouhani will soon be out of a job.