"We will," he insisted after a suicide bomber ravaged a crowded Tel Aviv bus, "solve it, if not tomorrow, then the day after tomorrow.''
Yet every blow of this kind makes his - and the PLO leader Yasser Arafat's - task more intractable. Mr Rabin was elected three years ago on a platform of "peace with security". His voters are less and less convinced that he is delivering. And the more insecure they feel, the more they turn to the right-wing opposition and its telegenic leader, Benjamin Netanyahu.
Mr Rabin stressed yesterday that he was suspending the peace negotiations only until after the funerals of the bus victims. Jews are normally buried within 24 hours of their death. But Mina Zemach, Israel's leading political pollster, suspects that the public will not be so easily appeased. "My impression," she said, "is that the public will demand a longer suspension until Arafat shows them that he can control the situation. There is a real fear now. It's not ideology. And this bombing will definitely increase that fear."
Even before the attack yesterday on the Number 20 bus, Israelis were worried about the army's redeployment from West Bank Arab towns that was supposed to be agreed by today.
In a poll earlier this month, Ms Zemach found that 64 per cent of Israelis were afraid that such an evacuation would increase the danger to their personal security and that of their families. At the same time between 50 and 60 per cent of Israelis want the process to continue. "They don't want it to stop, but they demand that Arafat control the terrorists," she said.
This is easier said than done. Much will depend on how Palestinians view the latest explosion, the first in Israel for six months. In that period Mr Arafat has been largely successful in persuading people in Gaza and the West Bank that he is doing his best and the delay in the withdrawal of Israeli troops is to be blamed on Mr Rabin.
Support for the Islamic militants of Hamas and Islamic Jihad has been static at about 20 per cent over the last 12 months, according to opinion polls. The degree of pressure Mr Arafat can put on them is in part a function of what Palestinian public opinion will accept.
Even then the bombers will be difficult to eliminate because the Islamic fundamentalist groups are not a united front. Islamic Jihad is badly split. Hamas, which is much the bigger organisation, is divided between those who support suicide bombing and those who want to launch their organisation as a political party.
Presumably, Mr Arafat will react by ordering a wave of arrests in Gaza, where he has 18,000 soldiers and police and the local Islamic leaders are well known, as he did earlier this year.
But Israeli public opinion is unlikely to be understanding about Mr Arafat's inability to give them total security.