But free access will only be given if the Palestinian leadership prevents militant attacks or they will suffer the consequences, he added on Saturday.
Speaking on Israel Radio, Peres said Israel had no intention of bottling the Palestinians in Gaza, but their future depended on the Palestinian leadership's ability to rein in fighters.
"We are not making Gaza into a prison, people will be able to leave Gaza and enter Gaza and within Gaza the roads will be open," he said. "Obviously in all these cases we shall attend to Israel's security needs.
"Palestinians have voiced fears that the closure of Rafah - their main gateway to the outside world - in addition to existing restrictions on entry to Israel and the lack of a harbour or airport, would lock up Gaza's nearly 1.4 million residents in the overcrowded coastal strip.
Also on Saturday, Aljazeera learned that four Palestinians were wounded, one seriously, when Israeli occupation troops opened fire at them in Bait Furik village east of Nablus.
Israeli forces had earlier stormed the village and civilian Palestinians pelted them with stones.
Strong response promised
Israel's military chief of operations, meanwhile, said Israel would react with extreme harshness to any attempted militant attacks from Gaza after the withdrawal, which is scheduled to begin on Sunday.
Suleiman (L) wants foreign
inspectors at the Rafah crossing
"An hour after we leave the field there will be a strategic change...in the nature of our response to even any attempt at terror," Major-General Yisrael Ziv told Israel Radio. "We shall have a far more extreme reaction to any attempt."While Israel has in the past used air strikes and tank assaults against resistance fighters, it declared a policy of relative restraint along with Palestinian resistance groups in February.
Egyptian intelligence chief Omar Suleiman is expected in Gaza on Sunday to try to wrap up a post-pullout border deal between Israel and the Palestinians for the Rafah crossing between Egypt and Gaza, which Israel closed earlier this week to the Palestinians' dismay.
Israel has agreed in principle to Suleiman's proposal to deploy foreign inspectors at the Rafah crossing between Egypt and Gaza when it reopens for passenger traffic, but says a final deal depends on how well the Palestinians combat fighter groups.
In an interview published in a Palestinian newspaper on Saturday, international Middle East envoy James Wolfensohn said the Israelis had agreed to Suleiman's Rafah plan, to be implemented within six months, but Palestinians were pressing for the crossing to be reopened sooner.
"Some Palestinians are wondering why it shouldn't be three months, or maybe one month or one week," Wolfensohn told Al Quds daily.
Wolfensohn: Rafah without Israeli
presence a major achievement
"They are forgetting that Rafah being in Palestinian and Egyptian hands, without an Israeli presence, is something they should be proud of as a major achievement. It should be the start for making economic progress."
Wolfensohn said Palestinians initially would travel between Gaza and the non-contiguous West Bank through Israel in escorted road convoys. No decisions have been made on a permanent travel solution, he said, but a rail link is an option.
Peres said the end of Israel's 38-year presence in Gaza gives the Palestinians an opportunity that must not be squandered.
"The Palestinians need to show that they are capable of controlling Gaza," Peres said. "This is the first time in the history of the Palestinian people where they have been given the opportunity to fully govern a defined territory."
He said valuable international aid pledged to the Palestinians would be at risk if law and order failed to prevail in Gaza.
"Who in the world will pay money or support the Palestinians if terror rules Gaza?" he asked.