The slight edge had Mr Peres' supporters dancing and waving olive branches while Mr Netanyahu's camp was downcast late last night.
"The results are against incitement, against violence and against the assassination of Prime Minister Yitzhak Rabin.," Moshe Shahal, the Minister of Internal Security, told a jubilant crowd at Labour's headquarters in Tel Aviv.
Mr Netanyahu said the result was still too early to call.
"It is still early. The night is still long," he told supporters at his Likud party headquarters. "We need to be patient. There are no final results yet. The race is very, very close."
Results in the Knesset (parliament) are clearer and show that both the governing Labour party and Likud have done badly. The smaller parties - notably the religious parties and the party representing the Russian immigrants - have done spectacularly well.
This means that if Mr Peres forms a government it will be farther to the right and less flexible than his present administration in agreeing terms with the Palestinians.
On the basis of early projections, Labour will win 35 seats in the 120- member Knesset, compared to the 44 seats it held before the election. Likud will have 32 seats (40). Labour's left-wing ally Meretz will have 11 (12).
"This shows there is a God," said Meretz leader Yossi Sarid in relief. The biggest change is seven seats for Yisrael B'Aliyah (Russian immigrants) which was formed by Natan Sharansky, the former Soviet dissident, only last year.
Mr Peres will look to Mr Sharansky and to the religious parties: the National Religious Party (NRP) won nine seats (six) and Shas nine (eight). His only potential allies on the left are the two Arab parties which won seven seats compared to five before.
Mr Peres appears to have been saved by the heavy turnout of Arab-Israelis, 77 per cent of whom voted, at the last minute.
It is is very unlikely, however, that the NRP would remove any Israeli settlements from the West Bank or compromise on Jerusalem in the interests of an agreement with Yasser Arafat, the PLO leader.
The Third Way, a Labour splinter group opposed to withdrawal from the Golan Heights was expected to gain three seats. Ironically the reform of the voting designed to weaken the religious parties has strengthened them.
Earlier, in the ultra-orthodox stronghold of Mea She'arim in the heart of Jerusalem, there was no doubt about the intense interest in the election. A taxi hired by one of the religious parties to being voters to the polls carried an enormous sign saying: "Only Netanyahu is good for the Jews."
This was denounced by Labour as a racist attack on the Israeli Arabs. Haim Ramon, Labour's campaign manager, warned that if Mr Netanyahu wins "you will once again live as second-class citizens".
For weeks Israeli politicians have focused on the wild cards of the Israeli election: ultra-orthodox, Russian immigrants and Israeli Arabs. This is because the election is so evenly balanced between the two main party leaders. Labour and Likud have focused almost exclusively on winning the prime minister's office, enabling smaller parties to make gains in the Knesset.
Meanwhile, there was controversy when the convicted killer of prime minister Yitzhak Rabin cast his ballot. A polling booth had been set up in for the inmates at the prison near Beersheba in the Negev desert where Yigal Amir is serving a life sentence for killing Rabin at a peace rally last November.
The 26-year-old student had hoped to stop the prime minister's policy of trading land for peace with the Arabs.
Rabin's widow, Leah, said it was "an unprecedented scandal" that her husband's killer was permitted to vote.
A Peres campaign advert published in Israeli newspapers yesterday showed a photograph of a grinning Amir, with the caption: "Don't let him win."
In Israel, inmates have the right to vote. Earlier this month, Israel's Supreme Court turned down an appeal by a private citizen to strip Amir of his citizenship and thus deny him the right to vote.Reuse content