But there appeared to be no evidence last night of where the man is being held, or whether he is still alive, 24 hours after the deadline set for his execution passed.
Throughout the West Bank and Gaza there was wide support for the kidnapping, carried out on Sunday by Hamas - the Islamic Resistance Movement - which yesterday celebrated the fifth anniversary of its launch, at the start of the Palestinian intifada.
It is the Hamas founder, Sheikh Ahmed Yassin, jailed by Israel last year, whose release is demanded in exchange for the soldier, Nissim Toledano. Yesterday Hamas offered to negotiate on a prisoner exchange. Israel's Prime Minister, Yitzhak Rabin, said Israel might talk if the kidnappers proved the soldier was alive.
For Israel, the Palestine Liberation Organisation (PLO) suddenly looks tame, now Hamas has shown what it can do. Islamic militants' influence in the occupied territories has been underestimated by Israel in the past, to counter threats from the PLO.
Now however, even Yasser Arafat, the PLO chairman, who is willing to talk about Palestinian autonomy in the West Bank and Gaza, looks reasonable next to Sheikh Yassin, who believes every Muslim must act to liberate 'all of Palestine' - in which he includes Israel - from the Jews.
While Mr Arafat is reining in his gunmen, Hamas has stepped up resistance and, while the PLO's political structures appear to be declining, Hamas is presenting itself as a body with a clear political profile.
The kidnapping will strengthen the argument of the Israel left-wing that it is time to talk directly to PLO leaders in order to strengthen PLO influence and counter Hamas' growing support.
Yesterday Benvamin BenEliezar, an influential cabinet minister, said that, effectively, Israel is already talking to the PLO through the local Palestinian leadership, who form the delegation to the Middle East peace talks - a point Israel is reluctant to concede publicly, because of its refusal to have PLO contacts.
Although the kidnapping may strengthen the PLO politically, it may have been damaged in other ways because of the credibility the hostage-taking has given Hamas on the streets.
Wearing their peace-delegation hats, the Palestinian leaders would be expected to condemn the kidnapping, but to do so would be to lose all credibility with their own people in the occupied territories. Not surprisingly, therefore, the PLO and the delegation have said nothing.