A group of 21 prisoners from the West Bank left Ofer prison, near al-Quds, shortly after 1:00 am (2300 GMT) Wednesday and the other five crossed moments later into the Gaza strip, correspondents at both sites said.
The West Bankers left Ofer in two minibuses with blacked-out windows and drove the short distance to the Beitunia crossing into the West Bank where they were greeted with cheers and fireworks.
They then drove to nearby Ramallah where they were welcomed at an official ceremony headed by acting Palestinian Authority Chief Mahmud Abbas, who said that talks would not bear fruit unless all of approximately 5,000 Palestinians held by Israel go free.
"There will be no agreement if so much as one Palestinian prisoner remains behind bars," Abbas told thousands of cheering Palestinians gathered outside his headquarters in the West Bank city.
Speaking before the army radio's report Abbas reiterated the Palestinians' denial that the prisoner release was part of an agreement to allow Israel more settlement building.
"There are some living among us who say that we have a deal (to release prisoners) in exchange for settlement building, and I say to them, be silent."
Last week, an Israeli official said new tenders were to be announced in the large settlement blocs and in East al-Quds "in the coming months" as part of "understandings" reached with both the Palestinians and Washington.
Wednesday morning's radio report said that Israeli Prime Minister Benjamin Netanyahu and Interior Minister Gideon Saar had agreed to build 1,500 new homes in the east Jerusalem settlement of Ramat Shlomo.
The five freed Gazans were met by hundreds of relatives and well-wishers as they entered the strip through the Erez crossing from Israel.
Netanyahu agreed to release 104 prisoners in stages as part of the resumption of talks in late July, after a three-year hiatus. A first tranche of 26 was freed on August 13.
Israel announced plans for more than 2,000 new settler homes in tandem with the August prisoner release, enraging the Palestinians.
The talks are held under a US-imposed media blackout but a senior Palestinian official said Tuesday that Israel had adopted hardline positions and negotiations had so far produced "no tangible progress".
"The current Israeli negotiating position is the worst in more than 20 years," Yasser Abed Rabbo, a top official with the Palestine Liberation Organization, said in a statement.
"They want security first, and that the borders of the state of Palestine should be set out according to Israeli security needs that never end, and that will undermine the possibility of establishing a sovereign Palestinian state."
Although Israel is engaged in direct peace talks with the Palestinians the prisoners' release has sparked tensions within Netanyahu's coalition.
Nineteen of the 26 freed Wednesday are members of the Fatah party led by Abbas, three are members of Hamas, and four are from the leftwing Popular Front for the Liberation of Palestine, according to a list released Sunday.