Regev told ABC News, "It is important to show the people that moderate leaders can deliver more tangible results than extremist leaders ever can."
Like Abbas, Palestinian Prisoner Affairs Minister Ashraf al-Ajami hopes to see thousands more prisoners freed.
He told Israel Radio, "We view today's prisoner release as a step in the right direction and we hope the Israeli government will negotiate with the Palestinian leadership about the next prisoner release when a list will be compiled by different criteria, so that all Palestinian prisoners will be released."
Al-Ajami has yet to determine what Israel will get in exchange for the prisoners' release.
"The release is part of the peace process," he said. "We hope this process will succeed and we'll arrive at peace, security and stability in the region."
Regev explains that Israel's gesture was done to accelerate the drawn-out peace-talks.
"We see this as an important confidence building measure," he told ABC News. "We understand the sensitivity of prisoner issues to Palestinian society, and we want to try to strengthen Palestinian pragmatics and to help with peace and reconciliation."