Haniya tells anniversary rally in Gaza City that peace talks have “failed”.
Abbas’s term in office was due to expire on January 25, with elections scheduled to be held on January 24.
But the January elections were postponed over differences between Hamas movement and Fatah faction.
The move aims to prevent a constitutional vacuum after January 24, when the present mandates expire, as Hamas has vowed to prevent a vote in their Gaza enclave.
Hamas has said it will not allow the vote in its territory until there is a national reconciliation agreement.
Divisions boiled over in June 2007 when Hamas took full control of the Gaza Strip after forcing out security forces loyal to Abbas.
Hamas dismissed the PLO’s decision as non-binding, accusing the council and Abbas of “political bribery.”
Fawzi Barhoum, Hamas spokesman said: “This is a new trick to grant legitimacy to Abbas by saying that everything (the presidency and the parliament) is in one basket.
“Abu Mazen’s (Abbas’s) term has ended and no one has the right to extend it. The parliament is its own master according to the political system and will continue to carry out its duties until there are new legislative elections.”
Abbas was elected on January 9, 2005 for a four-year term.
The Palestinian Authority extended his presidency by one year so presidential and parliamentary elections could be held on the same date, as required by Palestinian Basic Law.
Hamas does not recognise the extension.
Abbas said in November he did not wish to seek another term in the elections he had called for January because of his frustration with US-led peace efforts and Israel’s refusal to completely freeze settlement activity.