By Jonathan Marcus
BBC diplomatic correspondent
The low-level war between Israel and the militant Hamas group in the Gaza Strip has flared into a new upsurge of violence with Israeli strikes on Palestinian militants being met by a barrage of rockets fired into southern Israel.
Hamas and other militants cause terror on southern Israeli streets
Responding to this latest fighting Israel's Prime Minister Ehud Olmert, who is on a visit to Japan, offered his citizens little hope of an early end to the rocket attacks.
"This is a long process and a painful one and we haven't any magic formulas to solve this today," he said.
He repeated his threat against the Hamas leadership, asserting that "no-one in Hamas, neither among the low ranks nor among the senior ranks will be immune".
The Palestinians, he warned, were testing Israel's patience to the limit.
While the litany of attacks and apparent reprisals is familiar this is not a static conflict.
Hamas's goal appears to be to establish a balance of deterrence they hope will encourage the Israeli government to restrain its own forces
The Palestinian rocket fire is creeping slowly northwards in Israel, from Sderot just a mile from Gaza's border to Ashkelon 10km (six miles) away, as militants deploy better-manufactured and longer-range weapons.
Israeli military planners fear that in due course Ashdod 30km away could come under regular attack.
The Palestinians also seem to be able to stock-pile quantities of rockets; Wednesday's barrage of some 40-50 missiles providing a taster for the Israelis of the potential threat to come.
The strategy of the Palestinian militants is also becoming clearer.
They are well aware of the Israeli military's capabilities. Their goal appears to be to establish a balance of deterrence with each significant Israeli incursion or targeted killing meeting a significant response; one that they hope will encourage the Israeli government to restrain its own forces.
Mr Olmert and his ministers are under huge pressure to do something.
But none of the options facing Israel are appealing; least of all a major military operation into Gaza.
This would risk significant civilian casualties and even if it was successful, what Israeli analysts ask would they do then?
Nobody envisages a return to the occupation of Gaza, but engineering a new leadership there, handing the territory back to Fatah for example, seems fanciful.
No wonder opinion polls suggest that a clear majority of Israelis now appear to favour some kind of negotiations with Hamas.
While maintaining the military pressure on Israel, some elements in Hamas have been signalling a desire for some kind of pause or truce.
Militants seem able to stockpile quantities of weaponry
The reality is that Israel's tactical intelligence picture in Gaza remains remarkable and it has been able to repeatedly target senior Palestinian militants.
The Palestinian fighters are feeling the pain and Hamas too would like to avoid a major Israeli military incursion which it realises might well be very different from the failed Israeli operation in Lebanon two summers ago.
A pause or temporary truce though is seen by the Israeli government as a major risk.
It would allow Hamas to consolidate its position; allow militants to stockpile rockets in large numbers and, potentially, give Hamas a breathing space to try to expand its influence in the West Bank.
The trouble is though that Israel and indeed Washington's approach to Gaza has borne little fruit.
Isolating Hamas has served little purpose. Hamas has shown a remarkable level of political dexterity both in its initial assault against Fatah and, more recently, in organising the orchestrated break-out of Palestinians into Egypt. Both events appear to have taken the Americans and the Israelis by surprise.
There are signs that the terms of the debate are shifting in Israel
Hamas has been able to demonstrate that it can influence events and make life uncomfortable not just for the Israelis but for the Egyptians too.
It is the government in Gaza and it is very hard to see how living conditions there can be improved and any sort of normality achieved as long as Hamas is ignored.
That is why this latest Israeli opinion poll published by the Haaretz newspaper is so interesting.
Even half of the generally more conservative Likud voters backed some kind of talks with Hamas.
Some prominent security experts like the former Mossad chief Efraim Halevy also believe that a dialogue with Hamas should be explored.
There are signs that the terms of the debate are shifting in Israel. But it is hard to see how the Mr Olmert's government can change its line as long as the rocket fire continues.