Although Mr Peres immediately responded by saying that the peace process must continue, he also announced that he had broken off all contacts with the Palestinians "for the time being". Indeed, he could have done little else in response to what is already shaping up to be Israel's worst terrorist outrage and one that was deliberately intended to shock Israeli public opinion just as the electoral campaign begins.
A bomb on a bus, a peace process at risk and potentially profound consequences for a forthcoming election - the situation in Israel has uncanny echoes of that in Britain this week.
There is no doubt as to why the incidents in Israel have occurred. Hamas's military wing, the Izzedin Qassim Brigades, had warned as long ago as last December that they would exact revenge for the death of Yahia Ayache, the legendary master bomber known as "The Engineer", who was killed by a bomb concealed in his mobile telephone.
Nobody in the Gaza Strip, where it occurred, doubts that Israeli security forces organised the assassination, partly to restore public confidence after their lamentable performance in protecting Mr Peres's predecessor, Yitzhak Rabin, who had been assassinated by an Israeli extremist in November. The only surprise is that nothing had happened earlier, probably because Hamas was anxious not to embarrass Mr Arafat during the Palestinian elections in late January.
In the wake of those elections an air of complacency had developed, certainly in Israel, where the feeling had apparently spread that Hamas (weakened by its abstention from the electoral process in which over 80 per cent of Palestinians in the Autonomous Territories took part)was increasingly a spent force. Like the secular extremists in the PLO, it was said, Hamas's time had passed and its support among Palestinians had dropped dramatically - to 10 per cent or less. The Israeli government had, since the Rabin assassination, directed its attention towards its domestic opposition and towards pushing the peace process ahead with Syria. The elections in the Autonomous Territories had, it was felt, opened a new chapter for the Palestinians in which democratic process would replace violence.
The bombs in Jerusalem and Ashkelon - where the founder of Hamas, the blind Sheikh Yassin, is imprisoned - have destroyed those illusions. In short, militants connected with Hamas have not been cowed by recent events, nor have they abandoned their hostility to the peace process. They know, too, that Palestinian feelings about the peace process are still highly ambivalent; there is much anger over Israel's high-handedness and insensitivity - the repeated closures of the border with Israel have played havoc with the nascent Palestinian economy, with losses in earnings estimated at up to $6m each day and unemployment soaring to 30-40 per cent.
Many more people in the Autonomy sympathise with Hamas's condemnation of the peace process than the electoral figures would suggest. Hamas militants, therefore, are swimming in a sea of potential support despite Mr Arafat's condemnation of their latest action. Even the negotiations between the PLO and Hamas, said by Mr Arafat's assistant, Abu Ala, to have been intended to avoid further violence, have now been thrust to one side by Israel's demand that the Palestinians themselves find and punish the bombers without delay.
The simple fact is that many, inside Palestine and outside, feel increasingly outraged by the asymmetry of the peace process and thus find it difficult to completely reject the path chosen by the militants, despite its violence.
It is here that the crisis in the peace process now resides. Mr Peres, it is said, advanced the date of the Israeli legislative elections from October to May precisely to minimise the time available for incidents such as these bombings to take place. He has tried to capitalise on the wave of support his party's peace process policies have received inside Israel itself in the wake of the death of Mr Rabin.
Now, however, he has to face the uncomfortable fact that if the bombs continue to explode, his people's anxieties over security will outweigh any consideration of an untried peace with a traditional enemy. The pendulum might then very well swing back to the Likud opposition and to his rival for the premiership, Binyamin Netanyahu.
The prospect of a sustained campaign of bombings must haunt both Shimon Peres and Yasser Arafat. For Mr Peres, it would make the election virtually unwinnable, and would hand Mr Netanyahu a completely unexpected opportunity to stop the peace process dead in its tracks. For Mr Arafat, it would spell the end of an immediate prospect of a Palestinian state - apparently offered by Mr Peres's close assistant Yossi Beilin in the recent informal Israeli Palestinian discussions - and the threat of minimal Israeli concessions in the final status talks, with which he will have to agree if he wishes to salvage anything at all from the current crisis.
The Israeli government's dilemma is one that should be well understood in London, for its experience with Hamas is not so different from the British Government's experience with Sinn Fein and the IRA. Just as John Major assumed that in speaking to Gerry Adams he was talking to the IRA, so Shimon Peres seems to believe that Mr Arafat can dictate to Hamas and its militants - which the Hamas leadership almost certainly does not and cannot control. Like Mr Major, Mr Peres is attempting to force on a reluctant adversary a peace process that is essentially unacceptable. And like Mr Major, who has to deal with the irredentism of loyalist Ulster, Mr Peres now has the lowering spectre of a revitalised Likud, able to draw on disaffected Labour supporters as well as its own powerbase and a revived settler movement for whom the stain of Mr Rabin's assassination has been wiped away by the Jerusalem and Ashkelon bombings.
It remains to be seen, however, whether Hamas, like the IRA, is determined on a sustained bombing campaign to force its own views on to the peace agenda or whether Israel can, once more, nip the violence in the bud, either through its own efforts or by forcing Mr Arafat to act as its surrogate. But even if it does, there is still no guarantee that the whole tragic and horrific cycle will not break out afresh for this violence, in Ireland or Britain, as in Palestine or Israel, has a political significance that cannot be ignored.
The writer is deputy director of the Geopolitics and International Boundaries Research Centre.Reuse content