Thirty percent of respondents to the survey, carried out by Palestine's Birzeit University, said Ahmad Quraya's performance was "weak", while another 30% said it was "fair" and 25% said it was "good".
The poll, published on Wednesday, confirmed that the Palestinian Liberation Organisation's Fatah faction, headed by Yasir Arafat, remains the people's party of choice.
Thirty eight percent of respondents said they would vote for a bloc formed by Fatah if general elections were held, compared with 21% who said they would choose a list led by the Islamic group Hamas.
Fifty-seven percent of those polled said Arafat is "the best qualified person for the leadership of the Palestinian people".
However, the survey noted that support for Fatah has slightly declined since the beginning of the Palestinian uprising in late September 2000, while the number of Hamas sympathisers has climbed.
The survey was conducted on a sample of 1200 Palestinians in the West Bank and Gaza Strip and has a 3% margin of error.
Asked about the armed struggle against Israel's occupation of the West Bank and Gaza, 53.4% said they would support ceasing attacks against Israeli civilian targets providing Israel reciprocates.
Fourteen percent did not ask for any reciprocity, 30.8% opposed ceasing attacks, and the remainder did not express an opinion.
Palestinian Islamic groups have demanded Israel freeze its attacks, ostensibly aimed at rooting out and eliminating resistance fighters, as a precondition to declaring a ceasefire.
On the economic front, 78% said they live on less than two dollars a day or under the poverty line, according to the World Bank definition.
"I think this is probably an underestimate of the opposition to the Quraya government which has reached a stage of fiasco. It has not delivered on any of the aspirations of the Palestinian people."
Aljazeera.net Palestine correspondent
And nine percent said they no longer have any sources of income.
Khalid Amayreh, Aljazeera.net's correspondent in Palestine, said he was not surprised by the Palestinian people's verdict on Quraya.
He said: "I think this is probably an underestimate of the opposition to the Quraya government which has reached a stage of fiasco. It has not delivered on any of the aspirations of the Palestinian people.
"But we must not lose sight of the fact that Quraya's failure stems from the Israeli occupation of the West Bank and the Gaza Strip. He is not free to act, his hands are tied."
Amayreh added the poll's confirmation of Arafat as the most credible Palestinian leader was inevitable.
"Arafat has always eliminated any opposition to him so it is not surprising that people consider him to be the only credible leader," he said.
"Arafat is part of the problem and part of the solution. He is the main impediment to democracy and reform of Palestinian political institutions.
"On the other hand, he is the adhesive glue that keeps all the Palestinian factions together. In his absence, I think we would see the disintegration of Fatah."
And Amayreh said that support for resitsance group Hamas has grown, especially among middle class professionals in the occupied territories.
He said: "Hamas can now consider themselves second among equals with the Palestinian government."