Jerusalem (CNN) -- Thousands of Palestinians celebrated the release Sunday night of 550 inmates from Israeli prisons, part of the second phase of the deal that won the freedom of captured Israeli soldier Gilad Shalit.

The revelry in the Mukataa compound in Ramallah -- the long-timehome to the late Palestinian leader Yasser Arafat -- ran late into the night. Tayeb Abdel Rahim, general-secretary in Palestinian President Mahmoud Abbas' office, was among those officials greeting the line of freed prisoners, as they all paid their respects at Arafat's grave.

Hamas' armed wing, the Izzedine al Qassam Brigades, welcomed the news even as they, like Rahim and other Palestinian leaders, continued to push for the release of others in Israeli custody.

"It's a great accomplishment, but it's not the end," brigade spokesman Abu Obieda said Sunday night. "We will work toward liberating all our prisoners."

The Israel Defense Forces said in a news release Sunday night that the International Red Cross assisted in the release process, which it noted at 10:30 p.m. had been "completed."

It all follows a deal, signed between Israel and Hamas in October, that won Shalit's release from Hamas in exchange for allowing more than 1,000 Palestinians to leave Israeli jails.

A total of 477 prisoners were freed in October under the first stage of the swap.

Phase two happened late Sunday night with the departure of ten buses from Ofer Prison, said Sivan Weizmann of the Israeli Prisoners Authority.

The majority of the prisoners to be released Sunday -- 505, including four women -- were sent to the West Bank through the Beitunia crossing. Forty-one others were transferred into Gaza through the Kerem Shalom crossing. Two prisoners were sent to Jordan via the Allenby crossing and two others -- a man and a woman -- were sent to their homes in east Jerusalem via the Atarot base.

Rahim, the senior official in Abbas' office, thanked Egyptian officials for their role in the prisoner swap. He also said that Palestinian leaders are still seeking the release of others "including the old, children and the ill ones and also the members of the Palestinian legislative council."

"We insist that going back to the negotiation table will not happen without the immediate halt of all settlement activities ... and the recognition of the state borders, including Jerusalem, and the release of all prisoners as agreed to with the previous Israeli government," Rahim said.

Ahead of the expected release, Israeli security forces and hundreds of Palestinians clashed at a West Bank crossing near the internment facility where the prisoners were being held.

At least 20 Palestinians and one Israeli soldier were injured in the Sunday evening skirmishes at the Beitunia crossing, according to Palestinian and Israeli officials.

Samer Abu Ali, spokesman for the Palestinian medical relief services in Ramallah, told CNN that many of the Palestinians suffered injuries from inhaling tear gas and from rubber bullets fired by the Israeli security forces at the families and friends of the soon-to-be-released prisoners.

Palestinian independent lawmaker and political activist Mustafa Barghouti, who was at the scene of the clashes, told CNN that he had been sprayed with foul-smelling water used to disperse crowds and had been overcome by tear gas.

An Israeli military spokesman said some 400 Palestinians were engaged in an "illegal riot" at the crossing point and were throwing rocks and burning tires. The spokesman said soldiers were using riot control methods to disperse the crowds.

Shalit was captured in June 2006, and spent more than five years in captivity.

While the first stage of the deal to release him provoked significant discontent among some Israelis, with the families of terror victims claiming the price paid for one single soldier was too costly, Sunday's release prompted very little attention in Israeli media.

"The first group of prisoners released in October is immeasurably different from the one to be released today," Amy Palmor, head of the paroles department at the Israeli Justice Ministry, told CNN.

"All 550 freed today were not directly involved in the injuring or killing of Israeli citizens and most of them are members of Fatah," Palmor said. Fatah, the ruling Palestinian party, is considered in Israel as the most moderate of all Palestinian political fractions.

"The list in the first part of the deal was largely dictated by Hamas and was composed mainly of prisoners with blood on their hands serving life imprisonments. Most of them were members of Hamas and other extremist organizations," she added.

Many of the inmates who were released Sunday would have finished serving their sentences before the end of 2012, Palmor said.

But some criticized the terms of the swap agreement.

"This deal is a formality that doesn't meet our expectations. The second stage of this deal didn't include old, ill or handicapped prisoners. It also didn't include the remaining five female prisoners inside Israeli jails. This deal was solely controlled by the Israeli side," Issa Qaraqe, the Palestinian Authority minister of Detainees and Ex-detainees Affairs, told CNN.

"We will welcome and celebrate the prisoners in the Mukataa upon their release. The fact that the release will take place during the night will not affect our celebrations. Israel decided to release them at night with the wrong assumption that this will affect the intensity of the celebrations. The celebrations will start tonight and will continue for several days in different districts and towns, each prisoner will be celebrated in his own hometown," Qaraqe said.

The minister said Israel had launched a large arrest campaign after the initial prisoner release in October.

"As long as the occupation continues, arrests will continue," he said, adding that approximately 3,500 Palestinian prisoners remain behind bars in Israeli prisons.

CNN's Kevin Flower and Michael Schwartz contributed to this report