A Fatah member said the vote was simply "an attempt to sabotage the Egyptian effort to reconcile the Palestinian division".
The Basic Law, a forerunner to a Palestinian constitution, says that both president and parliament are elected to four-year terms.
But a loophole in the law, which Fatah is relying on, suggests that Abbas's term could be extended another year if it were deemed to be in the "national interest".
Hamas says Abbas's tenure as Palestinian president ends on January 8 [EPA]
Abbas was elected president in January 2005 but a year later Hamas defeated his movement by a landslide in parliamentary elections in Gaza.
Neither Hamas nor Fatah appear keen to share power in governing the Gaza Strip, which has been under Hamas control following a violent takeover in June last year, leaving Abbas with only nominal control of the occupied West Bank.
During Monday's vote, Hamas threatened to install Ahmed Bahar, the deputy parliamentary speaker, as Abbas's temporary successor if Abbas fails to announce a new presidential election by Wednesday.
Meanwhile, Khaled Mashaal, the exiled Hamas political leader, said talks with Israel over the possible release of an Israeli soldier have stalled and blamed Israeli negotiators for continuing to rehash previously-agreed issues.
He was quoted in Le Figaro newspaper on Monday blaming "a lack of reliability of Israeli negotiators" in discussions pertaining to Sergeant Gilad Shalit who was captured two years ago.