"There are some people who said we made a deal for accepting (Israeli) settlement ... I tell them to go away, because settlement is absolutely illegal," Abbas said after 21 of the 26 prisoners were released from the West Bank overnight.
"We are very happy for the release of the prisoners today," said Abbas. "We may hear some criticism here or there, but what matters is the releasing of one Palestinian, not those men talking nonsense on TV."
Recently, Abbas' Palestinian opponents told media that the president had secretly agreed with Israel to close his eyes to the ongoing Israeli settlement construction in the West Bank and east Jerusalem in exchange for the release of prisoners.
Under an agreement brokered by the United States, Israel agreed to release 104 prisoners, who were sentenced before the signing of the Oslo peace accords between Israel and the Palestinians in 1993, to prompt the resumption of direct peace talks after a hiatus of almost three years.
"The third group of prisoners will be released in two months, then the fourth group and the fifth group, until all prisoners are freed," Abbas said. "No permanent peace agreement would be signed as long as there is one single prisoner in Israeli jails."
According to official data, more than 4,500 Palestinian prisoners are still jailed in Israel.
Meanwhile, dozens of Palestinians and leaders of various factions gathered near the borders between northern Gaza Strip and Israel to welcome the freed prisoners.
Fayez Abu Eitta, spokesman of Fatah Party in Gaza, said "the happiness of today will be completed when all the prisoners are released from Israeli jails."
The peace talks between Israel and the Palestinians, which were resumed in late July, have so far achieved little progress on major issues such as settlement, refugees, status of Jerusalem, borders and security.
U.S. Secretary of State John Kerry, an architect behind the new round of peace talks, gave the negotiation a nine-month period to be finalized between the two sides.