Mr Abbas is due to complete his diplomatic tour with a trip to France.
Backed by European leaders, Mr Mitchell is urging Mr Abbas to give talks a chance.
Mr Abbas is a decent man whom the Americans, and the Israelis, can work with.
Mr Abbas said the endeavour was: "aimed at trying to breathe new life into the negotiations".
But the world will also watch closely how Mr Abbas treats the rival streams in Fatah.
Israel has shown some small signs of willingness to make Mr Abbas's job easier.
Mr Abbas made Mr Dahlan, Hamas's nemesis, secretary of a new national security council.
Mr Abbas said he had not given up on reconciliation but could not "wait forever".
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Mr Abbas has condemned it and urged the resumption of peaceful negotiations for an independent Palestine.
To complete his side of the deal, Mr Abbas has to rein in Palestinian militant groups.
Mr Abbas has expelled other rivals, such as Muhammad Dahlan, by banning their websites.
Still, if Mr Abbas has indeed decided to climb down, it will be a precarious operation.
Should the Americans and Europeans then balk, Mr Fayyad would look as silly as Mr Abbas.
But that will not help Mr Abbas in his quest to relaunch meaningful negotiations with Israel.
Should Mr Abbas dig in his heels for longer, some American intermediaries are looking at alternatives.
But for all the votes he won, Mr Abbas will find it difficult to do that.
That would be both a test of Mr Abbas and a sign of good faith.
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So Mr Olmert may survive long enough in his job to sign a deal with Mr Abbas.
Mr Abbas has reportedly come under pressure from Western nations including the US to scrap the bid.
Mr Abbas does have majority support for the road map among his Fatah movement, say Palestinian sources.
Sensing the region is swinging its way, Hamas is dismissive of Mr Abbas's outreach to the West.
That Mr Abbas now has a direct mandate from the Palestinian people should help him this time.
Mr Abbas came close to agreement with Ehud Olmert, a former Israeli leader, at least on borders.
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The parliament decided to hold a closed-doors session on Saturday to hear Mr Abbas's complaints about Mr Arafat.
Had Mr Abbas said yes, it might have been hard for a future Israeli government to back out.
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Though Mr Abbas lacked the guts to follow Mr Sharon's example himself, he can still stay on top.
For the moment it seems Mr Abbas, frustrated with a stalled Middle East peace process, has chosen the latter.
But Mr Abbas reiterated his demand that all construction in settlements be frozen.
Mr Abbas is faced with scepticism and division among his own people too.
However, a spokesman for Mr Abbas said the Palestinian leader had told Mr Obama the precondition remained in place.
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