Abbas argues that he has the right to remain in office for another year because the law says presidential and parliamentary elections should be held at the same time, the Jerusalem Post reported. Parliamentary elections are set for January 2010.
Hamas officials said they do not expect Abbas to step down while the war continues in Gaza. But they also deny his legitimacy.
"Thursday was Abbas's last day in office," said Osama Hamdan, who represents Hamas in Lebanon. "Our position on this issue is clear: Abbas's term in office has expired."
Mushir al-Masri, a spokesman for the party in Gaza, agreed.
"He doesn't have the right to speak on behalf of the people," Masri said. "He's in power only because the Israelis and the Americans want him to stay."
Abbas was elected in January 2005. A year later, Hamas won a parliamentary majority, although Israel and the United States refused to recognize its government.