Ghsain also said that the current Central Election Commission (CEC), which has five offices in Gaza, was no longer entitled to carry out preparations for an election, since Palestinian factions including Hamas and Fatah had agreed during unity talks that a new body should be formed.
However, Salih Rafat, a senior official in the Palestine Liberation Organisation (PLO), said on Wednesday that his group still hoped to persuade Hamas to participate.
"The leadership is now making calls to all the Arab countries to assume their role with Hamas to facilitate the holding of these elections," Rafat told the AFP news agency.
The elections were called after Hamas resisted signing a draft reconciliation pact with Abbas's Fatah movement, which would have set June 28, 2010, as the date for the polls.
Fatah and Hamas served in a unity government after the Gaza-based party won parliamentary elections in 2006, but after a political standoff between the two factions Hamas fighters forced Abbas loyalists out of the Gaza Strip in 2007.
Abbas responded to the takeover by dismissing the Fatah-Hamas unity government, resulting in two parallel administrations effectively ruling the two territories, while Egypt has attempted to broker a reconciliation.
The January 24 date set by Abbas corresponds with the end of the four-year term of the Palestinian Legilative Council brought in by the 2006 polls.
Abbas himself 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.
But Hamas has consistently rejected the extension granted to Abbas, and says it no longer considers him to be the legitimate president of the Palestinian people.