Mr Abbas' presidential term officially expired in January
Palestinian leader Mahmoud Abbas has announced that presidential and parliamentary elections will be held on 24 January.
His office said in a statement that the polls would take place across the Palestinian territories, including the rival Hamas-controlled Gaza Strip.
Mr Abbas's Fatah faction, which runs the West Bank, has so far failed to reach a reconciliation with Hamas.
The Palestinian leader's presidential term expired earlier this year.
Hamas officials said Mr Abbas's election call would deepen divisions between their faction and Fatah.
"This is an illegal and unconstitutional step because Abu Mazen's [Mr Abbas's] tenure is over and he has no right to issue any decree concerning this," Hamas spokesman Fawzi Barhum told AFP news agency.
Hamas won a landslide victory in the last parliamentary elections in 2006.
A bitter power struggle between Fatah and Hamas ensued, and in 2007 Hamas staged a violent takeover of Gaza.
The four-year term of the Palestinian Legislative Council, or parliament, is due to expire in January 2010 at which time fresh elections must be held, according to the Palestinian constitution.
In recent months Egypt has tried to broker a unity deal between the two factions.
Hamas has so far refused to sign up to Egyptian proposals accepted by Fatah, though Hamas officials have denied stalling on an agreement.
Mr Abbas had said he would call elections even if no unity deal was reached.