However, Al Jazeera's David Chater in Jersualem reported that another 68 of the men had been allowed back into the Gaza Strip after requesting that they be returned.
He also said that Palestinian sources has reported that the remaining men would be transferred to the town of Jericho, rather than Ramallah as earlier thought.
A senior official in Ramallah told the AFP news agency that Israeli authorities had given the go ahead for a group of about 30 men to cross to the West Bank.
The others still have to undergo questioning by the military before they will be cleared to travel. Those who are not allowed to travel will be sent to Egypt, the official said.
Ehud Barak, the Israeli defence minister, held talks with Palestinian officials on Sunday "in order to convince them to allow the refugees entry" to the West Bank town of Ramallah, his ministry said in a statement.
His request was followed by an urgent appeal to the Supreme Court by Israel's Human Rights Association on Sunday seeking to halt the return of the Fatah members on the grounds that there was a real threat to their lives in Gaza.
"Following meetings held throughout the day by the Israel Defence Forces [army] and the security establishment, the IDF is preparing to transfer the rescued Fatah operatives to the Ramallah area," the Israeli statement said.
"Israel and the IDF, both of whom operate according to humanitarian values in order to save lives, took action both on Sunday and again today, when a danger to the men's lives became apparent."
The men had sought refuge in Israel on Saturday at the Nahal Oz crossing after the bloodiest day of Hamas-Fatah fighting since Hamas took full control of the Gaza Strip last year, pushing out security forces loyal to Abbas. At least 11 people were killed and dozens wounded.
Abbas originally asked Israel to take in the Hilles clan and planned to transfer them to the West Bank, before he reversed his decision on Sunday. Monday's announcement marked another about face.
After the clashes last year, Abbas agreed to resettle about 250 of his Gaza loyalists in the West Bank.
The refugees each get $350 a month, in addition to government salaries, and Abbas' cash-strapped government covers rent for dozens of the most senior among them.