By Paul Reynolds
World Affairs correspondent, BBC News website
No immediate ceasefire is expected during the visit of the US Secretary of State Condoleezza Rice to the Middle East.
The Israeli-Lebanese border is key to a solution
However, she is trying to put together a package which might lead to one. Such a package could involve a new Security Council resolution, insisting on the implementation of an earlier resolution, 1559, from September 2004. That called for the disbanding of Hezbollah as a militia and the extension of Lebanese government control to the border with Israel.
The two missing Israeli soldiers --whose capture by Hezbollah was designed to start a negotiation for their release -- cannot be ignored. Israel and the US insists on a release. Hezbollah is still talking of an exchange.
A key element in a new resolution might be the formation of a more powerful international force in southern Lebanon to take over from the UN monitoring force Unifil.
Many questions remain about this concept. The idea of inserting a hostile force to control Hezbollah is not realistic.
If there is any hope that a cessation might come sooner rather than later, it lies in a shift in Ms Rice's language. Perhaps influenced by the images of civilian suffering, she is now talking of the need for an "urgent" ceasefire as well as the need for a lasting settlement.
The fact that Ms Rice went to Beirut on her way to Israel is another important signal that the earlier detached US attitude is being amended.
Israel too is saying it might accept some kind of international force in southern Lebanon. However Israel sees that as an interim measure before the Lebanese government asserts control.
However, that could all take time to put in place. And in the meantime the fighting goes on and the casualties mount.
The background to the US position is the neo-conservative agenda for change in the Middle East. This is not just a question of giving Israel time to hammer Hezbollah.
The Bush administration sees in this crisis the chance of enforcing change by breaking Hezbollah and through that diminishing Syria and, above all, Iran.
According to the New York Times, Secretary Rice will aim to detach Syria from Iran and try to get Syria to put pressure on Hezbollah - the approach heralded by President Bush in his overheard conversation with Tony Blair at the G8 summit.
Village by village
However, it is not going to be easy. On the ground, Israel is even now only fighting just over its border.
Israel could conquer the south, village by village, but its experience following its thrust to the Litani River some 20km north in 1978 (let alone its invasion to Beirut in 1982) was instructive.
It remained in Lebanon for another 18 years and learned that it can defeat but cannot occupy southern Lebanon.
It is possible therefore that this will drag on for some time to come with no clear-cut result, as the difficulties involved become clearer.
And at the moment Israel does not want to stop and nor, it seems, does Hezbollah.
European pressure frankly is not a major concern to Israel and certainly not a major hindrance. Israel is used to it and might have expected more of it.
An end to the fighting is likely therefore to take some time and already there is talk that Ms Rice will have to pay more than one visit. She has referred to setting a foundation only on this visit.
Civilian suffering is creating pressure for a ceasefire
But the ambition for change is there - in terms of Lebanon it is to get Security Council resolution 1559 fully implemented.
The Israeli hope is that this would provide it with a third border of agreed peace to join those of Egypt and Jordan, another milestone in its long struggle to establish itself in the Middle East.
In regional terms, the US ambition is to reduce the power of Hezbollah's supporters Syria and Iran.
Syria's power in Lebanon has already been cut down but Iran, especially with its nuclear programme in active dispute, is a thorn in US flesh.
If Iran can no longer perform the role of Hezbollah's protector and provider, then its ability to play a role in the region is much less.
That, in the eyes of the US administration, is a goal worth pursuing.