By Jonathan Marcus
Diplomatic correspondent, BBC News
First Washington, then Cairo and Amman, and on Monday it is the turn of London.
Israel wants to fix its own borders - without negotiating
Israel's new Prime Minister Ehud Olmert has taken his convergence plan on a road-tour.
He is trying to win international backing for a proposal by which - in the absence of a Palestinian partner - Israel will set de facto borders of its own making.
So far the reception has been mixed. There has been outright opposition in the Arab capitals and two, rather than three cheers even from President George W Bush in Washington last month.
He praised Mr Olmert's "bold ideas" but urged him first to seek negotiations with the Palestinian Authority (PA) President Mahmoud Abbas.
Mr Olmert is likely to hear a similar message from Mr Blair - combined with a plea for Israel to do everything it can to improve the quality of life for the Palestinians.
They are facing a triple crisis.
The Palestinian economy is collapsing following the suspension of direct aid to the PA from the US and the European Union in the wake of the Hamas victory in January's election. It is this aid which pays government salaries on which a significant proportion of the population depends.
The Palestinian are facing both political and economic crises
And so far the Europeans have not found a mechanism to reconcile their determination to keep Hamas at arm's length with their desire to avoid hurting ordinary Palestinians.
There is a political crisis - the growing rivalry between Mr Abbas and his Fatah movement on the one hand, and the Hamas-dominated Palestinian Authority on the other.
And if all this was not bad enough, there is now also the danger of military escalation, with Israel and Hamas squaring off against each other, in the wake of the deaths of eight Palestinian civilians, killed last Friday, apparently by an errant Israeli shell.
Mr Blair will be urging caution and pressing Mr Olmert to give the Palestinian leader a chance.
Mr Olmert realises that if his proposal is to gain even tacit international support, he must take time to test out what Mr Abbas might be able to deliver
Mr Olmert realises that if his proposal - it is far too early really to call it a plan - is to gain even tacit international support, he must take time to test out what Mr Abbas might be able to deliver.
Most Israeli commentators, though, see the trial of strength between Mr Abbas and Hamas as an essentially internal Palestinian affair.
Israeli analysts argue that the "prisoners' plan" which Mr Abbas wants to put to a referendum is not so much a peace plan between Israel and the Palestinians but one designed to bring about internal peace within the broader Palestinian constituency.
Caution on Iran
While in London Mr Olmert will also touch on Iran and its nuclear programme.
Despite some claims to the contrary, Israel has been playing a very cautious role, eager to avoid taking too prominent a part in the debate.
Times have changed since the days when Israel alone struck at Iraq's fledgling nuclear programme. The international context is very different.
And Mr Olmert's message will be that the Iran nuclear dossier represents not so much a problem for Israel, but one with which the whole international community must grapple.