At its final session on Monday, the Palestinian parliament empowered Abbas to appoint a new, nine-judge constitutional court that would have the authority to resolve any dispute between him and the incoming Hamas-dominated parliament or cabinet.
Hamas reacted vehemently to the decision, calling it "a bloodless coup".
Also on Monday, an executive decision was issued to place radio and TV broadcasts under the authority of the president's office, the Palestinian Maan News Agency said.
Hamas won 74 of parliament's 132 seats in landmark elections in January, ousting Abbas's long-ruling Fatah and touching off Western threats to cut off hundreds of millions of dollars in needed aid unless the group abandoned violence and recognised Israel's right to exist.
A Hamas prime minister could complicate any Middle East peace effort, because Israel and the United States have said they will not talk to members of the group, whose charter calls for the destruction of Israel.
Abbas, whose Fatah faction was voted out of government, has good relations with Washington and would be expected to take the lead in future negotiations.
Earlier on Monday, a spokesman for Hamas said the group had chosen the future prime minister but declined to disclose the appointee's name.
Several sources close to the Hamas deliberations for a new prime minister said Ismail Haniyeh, head of Hamas's parliamentary group, was a top contender.
Haniyeh is a pragmatist who survived an Israeli air strike in 2003 that targeted Hamas's leadership. But his militant background could be a further provocation to the United States.
Hamas has masterminded more than 60 bombings against Israelis since a Palestinian uprising began in 2000, but has largely adhered to a truce declared last March.