The largest release of Palestinian prisoners by Israel in a decade brought emotional scenes as the newly freed men were reunited with their families.
Israel was careful about which prisoners it released
As the first of the 500 to be freed stepped off buses, some gave the "V for victory" sign while crowds of relatives reached out to touch and hug them.
Israel says it will release a further 400 as part of a ceasefire deal agreed by the two sides earlier this month.
But Palestinians are critical that only less controversial inmates were freed.
They have demanded Israel free many more of the estimated 7,500 Palestinians still held in its jails.
Handcuffs and smiles
The prisoners freed on Monday were placed, handcuffed, onto several buses at the Ketziot military jail in the Negev.
Some smiled as they were transported to various checkpoints on the edges of the West Bank and the Gaza Strip and transferred to Palestinian Authority control.
Gunshots were fired and the flags of Palestinian militant groups were waved as prisoners were reunited with their relatives in scenes of tears and joy.
"I cannot believe that I'm smelling the air of freedom, that I will see my family," Abu Madala was quoted by Associated Press as saying.
"Nothing can describe my joy and my feelings."
Shortly afterwards, more than 50 released Palestinians travelled to Ramallah for a meeting with Palestinian leader Mahmoud Abbas.
"We are very happy with the release of this first group but it is only the start," Mr Abbas told them.
"You know that the prisoners question is at the top of the list of our priorities in negotiations [with Israel] and we will spare no effort to empty the prisoners."
The latest batch of releases is the largest in almost a decade and aims to boost Mr Abbas' position following his recent election as head of the Palestinian Authority.
However, the BBC's Barbara Plett in the West Bank city of Hebron says Palestinian officials stayed away from the reunions in protest at what they see as an inadequate gesture.
Most of those freed had already served at least two-thirds of their sentences, and none were involved in fatal attacks on Israelis.
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Mr Abbas has been under pressure from Palestinian militant groups to secure large-scale prisoner releases to win their backing for a fragile ceasefire declared at Sharm al-Sheikh on 8 February.
On Monday, Palestinian Prime Minister Ahmed Qurei presented the new 24-member cabinet to the Palestinian parliament for approval.
Key changes include the appointment of Nasser Yousef as interior minister, a move previously resisted by Mr Abbas' predecessor, Yasser Arafat.
Arafat's nephew, Nasser al-Kidwa, was named foreign minister, replacing Nabil Shaath, who becomes deputy prime minister.
However, a vote giving parliament's approval was delayed after it became clear that MPs wanted to see more faces in the line-up not tainted by Arafat-era corruption.