Jerusalem (CNN) -- Palestinian inmates began leaving Israeli jails early Tuesday, setting in motion the historic swap that will trade more than 1,000 Palestinian prisoners for one captured Israeli soldier.
A total of 477 prisoners were being moved to meeting points with the Red Cross, according to a spokeswoman at Israel's Prison Authority.
Israeli radio reported that more than 1,000 police officers were deployed to ensure public order and the safety of the convoys, which headed to the Egyptian border.
Late Monday, the Israeli Supreme Court rejected appeals against the release of prisoners in exchange for captured Israeli soldier Gilad Shalit.
Israel and Hamas approved the deal last week, agreeing to release in two stages 1,027 Palestinian prisoners, including hundreds serving life sentences for attacks on Israelis.
The second stage is scheduled to happen later this year.
Shalit has been held incommunicado by the Palestinian Islamist group Hamas, which controls Gaza, since his seizure.
The Israeli public overwhelmingly supports the swap for Shalit, an Israeli army sergeant who was abducted in a raid in 2006, when he was 19 years old.
Israelis are equally split on whether "the release of terrorists" will harm Israeli security, with 50% saying "Yes" and 48% saying "No" -- a statistical tie given the number of people polled.
Prime Minister Benjamin Netanyahu wrote to the families of terror victims to say he understood their pain.
"You were in my thoughts during the many uncertainties that have accompanied me in the negotiations," he said in the letter, which was released by his office.
"The decision regarding the release of Gilad Shalit is one of the hardest I have taken ... I understand the difficulty in digesting that these villains who committed these crimes against your loved ones will not be paying the full price that they deserve to," Netanyahu wrote.
But, he said: "The state of Israel does not abandon its soldiers and its citizens."
Nearly eight out of 10 Israelis favor the deal, according to the poll of 500 people conducted by the Dahaf Polling Institute for the daily Yedioth Aharonoth.
The families of some Palestinian prisoners being released had mixed feelings about the swap, they told CNN.
Mohamad Abu Khalil, whose son Ayman got three life sentences plus 90 years in jail, is glad his son is being freed -- but said he won't be coming home.
"It's better that Ayman is going to be released from Israeli jails, but sad that he won't be around his family here. It's better to be transferred to another country than being in Israeli jails," his father said.
The official Israeli list of prisoner releases lists him as being sent "abroad," rather than to Gaza or the West Bank, without specifying where.
The Israel Defense Forces declared a number of sites connected to the prisoner transfer and Shalit release to be closed military zones as of Monday.
The prisoners list released by Israel features 477 names, including those of Ahlam Tamimi, serving life terms for being an accomplice in the 2001 bombing of a Sbarro pizza restaurant, and Amneh Muna, who plotted the killing of a 16-year-old Israeli boy in 2001 and received a life sentence.
The most notable name not on the list is that of jailed Palestinian lawmaker Marwan Barghouti, who is serving five life sentences.
He was convicted in an Israeli court on murder and other charges related to his role in planning attacks on Israelis during the second Intifada.
Israel's Prisons Authority said the Palestinians slated for release are being taken to two facilities -- one for the 27 female prisoners on the list, the rest for the men -- from which they will be released together.
Once freed, they will be under various restrictions on a case-by-case basis: Some will not be allowed to leave the country, while others will have other restrictions on their movement or be required to report their whereabouts to local police, Justice Ministry spokesman Moshe Cohen told CNN.
Shalit, meanwhile, will be transferred back into Israeli territory via the Kerem Shalom border crossing and will undergo medical tests and debriefing at an air force base, the Israeli military said.
Once that is complete, he will be flown to his home at Mitzpe Hila, north of Haifa.
CNN's Guy Azriel, Kareem Khadder, Michal Zippori and Kevin Flower contributed to this report