Nabil Amr, the Palestinian information minister, is quoted by Reuters as saying Mahmud Abbas may stand down if he is not given more control in the security and administration fields.
Abbas is due to address a Palestinian parliament meeting on Thursday when he will report on his performance four months after being appointed under international pressure.
But in an interview with Aljazeera on Wednesday, Amr denied making the comments.
No confidence vote
And Michael Tarazi, an official spokesman for the Palestine Liberation Organisation, said although Abbas would not quit he might face a no confidence vote.
He told Aljazeera.net: "There is no way of knowing whether there will be a no confidence vote because it takes 10 MPs who want it to table a motion, and we are not even aware of one MP who has done that.
"But I think Abbas would welcome a vote because he will be confident of surviving it. It would serve to give him further democratic legitimacy in the eyes of the Palestinian people."
Tarazi also denied there was a power struggle between Arafat and Abbas.
Rumours that Arafat and Abbas are engaged in a struggle over Palestinian security services are widespread.
Arafat recently appointed his former rival and head of security in the occupied West Bank, Jibril Rajub, as head of national security services.
Strongman Rajub is perceived to be an opponent of Abbas.
But Tarazi said the rumours are an exaggeration.
"I think Abbas would welcome a (no confidence) vote because he will be confident of surviving it. It would serve to give him further democratic legitimacy in the eyes of the Palestinian people"
"There may be disagreements but that is an internal Palestinian issue. We have a democratically elected president and a prime minister who has the backing of the parliament so we are equipped to sort out the issues without there being a power struggle."
Abbas's address to the Palestinian parliament on Thursday will concentrate on the progress he has made on the peace process.
The so-called "road map" to peace was drafted by United States, United Nations, European Union and Russian officials.
The first stage of the plan called on the Palestinian side to end all violence unconditionally and implement administrative reforms.
It also charged Israel with normalising Palestinians’ lives, improving their humanitarian situation, freezing all settlement activity, and withdrawing from areas occupied since September 2000.
The second and third stages foresaw the establishment of a provisional Palestinian state, and international talks to settle finally the issues of borders, Jerusalem, refugees and settlements.
But the blueprint has failed to move beyond the first stage.