It is nothing like the lead Mr Peres enjoyed before the first bombs exploded on 25 February, but it is much better than his Labour Party feared.
His fortunes have revived primarily because there have been no more bombs and he has received heavy support from the US, most clearly expressed at the "summit of peacemakers" - prompted by the suicide attacks - in Sharm el-Sheikh.
A second poll, by the Dahaf Centre, shows Mr Peres has a lead of just 2 per cent, underlining that both Labour and the Likud opposition have everything to fight for during the two-month-long campaign. The Prime Minister has the advantage of incumbency, but Mr Netanyahu has improved his chances by persuading two right-wing rivals, General Rafeil Eitan and the former foreign minister David Levy, to withdraw their candidacies.
Both Mr Peres and Mr Netanyahu have stepped towards the political centre in recent weeks in order to win undecided votes. The Prime Minister speaks well of demolishing Palestinian houses, deportations and sealing off the occupied territories. The Likud leader has good things to say of the Oslo accords with the Palestinians, which his party platform opposes. Mr Netanyahu has still not wholly shaken off the damage done to him by the assassination of Yitzhak Rabin in November. But many Israeli voters always distrusted Mr Peres on security and this distrust has increased because of the suicide bombs.
Israeli polls can be deceptive because the electorate is not uniform. Mr Netanyahu will win almost all the ultra- orthodox Jewish vote and the Prime Minister will be supported by all Israeli Arabs.
To win the battle to be Prime Minister - who is to be directly elected for the first time - the right must have a 10 per cent lead among Jewish voters but, at present, is ahead by just 4 per cent.
The Labour tactics are becoming clear: play up separation of Israelis and Palestinians as an objective of the peace process and emphasise that "Hamas wants Likud to win". Likud on the other hand will argue that the Oslo accords have produced more, not fewer, Israeli dead.
The fighting in Lebanon, which has preoccupied the Israeli media in recent days, is unlikely to win or lose many votes but commentators repeatedly stress that another Hamas bomb in Israel could finally destroy Labour's chances. It is also true that the radical right has not changed its views, although it has been more discreet since Mr Rabin was murdered. Mr Peres says that the Shin Bet security agency has told him that there are thousands willing to kill him in order to prevent Israel withdrawal from the West Bank.