Palestinian President Mahmoud Abbas, who has called for new elections, would face a tough race against a contender from the rival Hamas group, according to a poll published Sunday. If presidential elections were held now, Abbas, leader of the Fatah Party, would win 46 percent, compared to 45 percent for the most popular Hamas politician, Prime Minister Ismail Haniyeh. However, in a separate contest for parliament, Abbas' Fatah movement was widening its lead over Hamas, winning 42 percent of the vote, compared to 36 percent for Hamas. In September, Fatah was ahead by 3 percentage points, at 41 percent. The survey was conducted by the independent Palestinian Center for Policy and Survey Research among 1,270 Palestinians and had an error margin of 3 percentage points. The questioning was concluded Saturday, the day Abbas announced he is calling early presidential and parliament election. Most of the respondents gave their answers before Abbas made the announcement, said pollster Khalil Shekaki. Sixty-one percent of respondents said they are in favor of holding new elections, while 37 percent said they oppose the idea. Many Palestinians want a new vote "because they are dissatisfied with Hamas, and even more so with the president," Shekaki told The Associated Press. In the presidential race, Fatah's strongest contender would be Marwan Barghouti, the Palestinian uprising leader jailed by Israel. Barghouti would win 57 percent of the vote, but in a very unlikely lineup, against the exiled supreme leader of Hamas, Khaled Mashaal. Barghouti could run from jail, but has not announced his plans. Shekaki said a third candidate would take away votes from Abbas and ensure the victory of a Hamas candidate. In the 2005 race, in which Abbas was elected, several independents had entered the race, but Hamas did not participate. Even in the parliament race, Fatah's lead of six percentage points is not a comfortable margin, Shekaki said, adding that Hamas could win both races if the Hamas-led government improves its performance. "There is a high probability for Hamas to win both elections," he said.