The gunmen fled the Palestinian-run Jneid Prison in the West Bank city of Nablus on Friday, after complaining that they had been beaten by guards.
The governor of the Nablus district, Jamal Muhaisen, appealed to the fugitives over a local radio station Saturday to return to prison voluntarily, citing concern for their safety.
Under the amnesty deal, hundreds of Palestinian gunmen have been removed from Israel's wanted list, provided they renounce violence and serve a transition period in Palestinian lockups. Last month, a Nablus gunman who left prison for a day, in violation of the agreement, was shot dead by Israeli undercover troops.
In an interview with a local Nablus radio station, Muhaisen said the 12 would be safer if they returned to the lockup. Muhaisen ended the conversation when the leader of the fugitives, Mahdi Abu Ghazaleh, came on the line. The governor said he didn't want to negotiate through a radio broadcast.
Israel has not commented on the breakout. Palestinian President Mahmoud Abbas has pledged to rein in militants and stop violence, as part of his commitment to the U.S.-backed "road map" peace plan.
The fugitives are from the Al Aqsa Martyrs' Brigades, a violent offshoot of Abbas' Fatah movement.
They've been held at Jneid Prison since January. They complained that they were beaten with clubs by guards following a fight among detainees.
Al Aqsa was founded after the outbreak of the second Palestinian uprising in 2000. The group was mainly involved in roadside shootings of Israeli soldiers and settlers, but was also responsible for several bloody attacks in Israel, including suicide bombings.
In other developments, the Islamic militant Hamas claimed responsibility Friday for firing shots at a group of Israelis and Canadian visitors touring near the border fence with Gaza. An aide to Israeli Public Security Minister Avi Dichter was wounded in the incident.
Other militant groups also claimed responsibility for the attack, including Al Aqsa and two little-known radical Islamic groups inspired by al Qaida, the Army of the Nation and Protectors of the Homeland.
Canada's foreign minister, Maxime Bernier, condemned the sniper attack on the group, which included members of the Board of Directors of the Canada-Israel Committee. "These attacks targeting civilians are unacceptable," she said.
Moshe Ronen of Toronto, chairman of the committee, said the group was learning about near daily rocket attacks on southern Israel fired by militants in the Gaza Strip.
"Within a few seconds of the sound of the shooting we understood we were being fired on," Ronen said. "The secret service of Minister Dichter told us to get down on the ground and both the minister and I were pushed to the ground and had our heads in the sand and didn't move for about ten minutes."
The group moved behind a concrete wall and was evacuated 90 minutes later, he said.
"It's a miracle that no one in our own group was injured or killed," Ronen said.
Gaza militants have fired rockets at Israeli border communities since late 2001, killing 13 people, severely disrupting daily life and provoking harsh Israeli retaliation. With Egyptian mediation, however, there has been a lull in recent weeks.