Israeli police went on high alert yesterday, setting up roadblocks outside major cities and reminding the public to look out for suspicious packages.
This followed concern that Sunday's car bombings in northern Israel could mark the start of a new campaign of Islamic extremist violence.
A series of suicide attacks derailed peace-making efforts in the mid-1990s.
But both Israeli and Palestinian leaders were adamant that the bombers would not prevail this time.
Provided the Palestinian Authority worked in partnership with Israel to try to thwart the attacks, said aides to Israel's Prime Minister, Mr Ehud Barak, there would be no reason to halt the renewed peace effort, which was cemented on Saturday night with the signing of the new Sharm al-Sheikh peace deal.
So far, said the Deputy Defence Minister, Mr Ephraim Sneh, co-operation between Israel and the Palestinian Authority was firm and productive.
In that light, Israeli and Palestinian legal teams met yesterday and concluded a deal to set up a "liaison office" to handle legal difficulties.
These would encompass disputes over such matters as car thefts and insurance claims, which often get bogged down in the bureaucracy of the two separate legal systems.
The Palestinian Authority President, Mr Yasser Arafat, condemned the Sunday night bombings, declaring that "terrorist attacks should be fought."
Three men died in the blasts, which occurred minutes apart in Tiberias and Haifa. The dead men, police indicated, were the bombers themselves.
Police had five people in custody last night suspected of helping to prepare the attacks. Some reports suggested that members of Israel's Arab minority, rather than Palestinians from the West Bank or Gaza, might have been involved.
Some members of the Likud opposition party have called on Mr Barak to suspend implementation of the Sharm deal, under which Israel is next week to begin a phased series of Palestinian prisoner releases and West Bank land handovers.
Two members of Mr Barak's own ministerial team, indeed - the National Religious Party leader Rabbi Yitzhak Levy and the immigrant leader, Mr Natan Sharansky - voted against the deal when it was placed before the cabinet on Sunday night.
And Rabbi Levy protested yesterday that Israel could not simply shrug off the blasts and proceed with "business as usual".
Tellingly, though, 21 cabinet ministers voted for the new accord. Particularly significantly Jerusalem's mayor, Mr Ehud Olmert, himself a Likud hardliner, backed Mr Barak in proceeding with its implementation, despite the new attacks.
"There were graver attacks in the past," when the Likud's Mr Benjamin Netanyahu held power, the mayor noted, and yet peace talks continued.
Though determined to rebuild relations with the Palestinian leadership that were all but destroyed during the Netanyahu era, Mr Barak was a critic of some aspects of past peace deals. As a former chief of staff, he is acutely sensitive to any perceived threat to Israeli security.
Thus, in the renewed atmosphere of tension created by Sunday's bombs, Mr Barak is certain to press Mr Arafat to uphold Palestinian commitments under the new deal - including the confiscation of illegal weaponry in Palestinian-held areas.
Also yesterday the Israeli Supreme Court, in a decision of immediate significance in the light of the bombings and arrests, effectively outlawed the use of torture by the Shin Bet security service in the interrogation of detainees.
The unanimous nine-judge ruling overturned a government commission decision, in 1987, which allowed the use of "moderate physical pressure".
In essence, that has meant such practices as interrogators depriving detainees of sleep, shaking them violently and tying them up for long periods.
Human rights groups have long campaigned against such methods; investigators justified them as the only means to "break" suspected militants and obtain information necessary to prevent acts of violence.
"Violence directed at a suspect's body or spirit does not constitute a reasonable investigation practice," the court ruled. "We are aware that this decision does not ease dealing with the reality (of security threats).
"This is the destiny of democracy, as not all means are acceptable to it, and not all practices employed by its enemies are open before it."