RAMALLAH, West Bank, Feb 17 (Reuters) - Palestinian President Mahmoud Abbas said on Thursday that an election promised by September would not be held if Hamas refused to allow voting in the Gaza Strip.

The election promise was issued on Saturday by the Palestine Liberation Organization in an apparent bid to head off any wave of popular protest fanned by the uprisings elsewhere in the Middle East.

But Abbas said he could not divide Palestinian territory.

Elections should include the West Bank and Gaza, and without that we cannot hold elections, the president told a news conference.

Hamas, an Islamist movement opposed to peace with Israel, controls the Gaza Strip. Abbas's Palestinian Authority holds sway in the West Bank. The two territories, which would form a single state under a peace treaty with Israel, are separated by Israeli land.

Abbas's comment, following talks with visiting East Timor President Jose Ramos-Horta, coincided with planned demonstrations in the West Bank's main city, Ramallah.

Unlike Tunisia, Egypt, Bahrain or Yemen there does not appear to be a strong anti-government groundswell among Palestinians. Their main frustrations are over the unending split between Hamas and Abbas's Fatah movement and the lack of progress towards a peace that will end Israeli occupation and finally give them a state of their own.

The demonstrators might say, 'we want elections', well, we are ready for elections. The demonstrators might say, 'stop negotiating with the Israelis', well there are no negotiations with the Israelis, said Abbas aide Nabil Abu Rdainah.

Why does Hamas say no? Why is no one criticizing Hamas over this? he told Reuters on Wednesday. Whenever there is a problem you have to go back to the people. That is democracy, that is what we are doing, but Hamas is refusing to cooperate. We cannot (hold elections) in the West Bank alone. They will say we are trying to divide the country and make two states.

Abbas's Palestinian Authority at the weekend said the spirit of change in Egypt should inspire Palestinians to unite.

The Palestinian leadership decided to hold presidential and legislative elections before September, senior Abbas aide Yasser Abed Rabbo told reporters.

It urges all the sides to put their differences aside, he said, referring to the bitter rivalry with Hamas.

But Hamas quickly turned down the proposal. Spokesman Fawzi Barhoum said the Western-backed Abbas, who has served as president since 2005, lacked the legitimacy to make such a call.

Hamas will not take part in this election. We will not give it legitimacy. And we will not recognize the results, Barhoum said on Saturday.

The last Palestinian presidential and legislative elections were held in 2005 and 2006, when Hamas won power in a surprise result. A unity government was short-lived and Hamas fighters in 2007 drove Fatah forces out of Gaza, seizing control of the enclave.

(Additional reporting by Crispian Balmer, editing by Douglas Hamilton)