"The presidential election is illegal," Mahmud Zahhar said as he entered talks with the new head of the Palestine Liberation Organisation Mahmud Abbas.
He added, "This election is a continuation of the Oslo process which has already failed and is finished."
The announcement had been widely expected as Hamas has consistently rejected the 1993 Oslo accords, which paved the way for the creation of the Palestinian Authority.
The smaller movement Islamic Jihad had confirmed on Monday that it would not contest the election slated for 9 January.
The decision by Hamas is a major boost to Abbas' hopes of being voted in as a replacement for Arafat who won the first and only presidential election in 1996.
Boost for Abbas
The dominant Fatah faction is understood to have agreed on Abbas as its candidate in the election but faces opposition from the Al-Aqsa Martyrs' Brigades, which has chosen Marwan al-Barguthi.
While polls show that Fatah remains the most popular of the Palestinian parties, its support has been eroded in recent years amid growing disillusionment at the performance of Arafat's administration.
Some polls have shown that Hamas now enjoys more popularity than Fatah in Gaza.
Ismail Haniya, another senior member of the organisation in Gaza, told Aljazeera that Hamas sought elections that would secure the rights of Palestinians
"This election is a continuation of the Oslo process which has already failed and
Gaza unit Hamas leader
"The forthcoming elections would only bring the same leadership of the Palestinian Authority that signed the Oslo accords and accepted the so-called road map peace plan," Haniya said.
"We seek to have elections that would enhance Palestinian national unity, and the election of a leadership that would strive to restore Palestinian rights, end the occupation of our lands and secure the right of Palestinians to return to their homes."