Speaking during an election rally in the town of Dura, 45km southwest of Jerusalem, on Friday, al-Barghuthi said Palestinians should not trust "biased and tendentious polls", an allusion to recent opinion surveys which gave Abbas a substantial lead over al-Barghuthi and other candidates.
"The results of the municipal elections prove that all the opinion polls we had seen were false. So don't trust these polls," he said.
"Instead, I urge you to work with me to create a new leadership that will feel and identify with the pain of our people, not the pain of others."
Those remarks were an implicit reference to Abbas' Aqaba speech of 4 June 2003 in which he, then Palestinian Authority (PA) prime minister, said he understood and was saddened by the suffering Jews had endured throughout history.
Al-Barghuthi said Palestinians on 9 January will choose not only a person but an approach, a system of thinking and a plan of action.
Abbas' pro-western image does
not go down well with all voters
"It is not a matter of choosing between two personalities and two characters," he said.
"What you have to do on 9 January is to choose between two approaches, an approach based on concession and capitulation, and another approach based on clinging to our national constants and inalienable rights."
Al-Barghuthi added: "We don't need a leader who will control us, because we are all languishing under the Israeli occupation. We need a leader who will lead us to freedom and liberation."
He said he was not running against Fatah per se, saying the movement had in its ranks "many good and patriotic people".
"But I represent the silent majority which is thirsty for ending this shocking subservience to Israel."
Lamb and tiger
Al-Barghuthi said Palestinians should never agree to sit down alone with Israel at the negotiating table.
"This is like entrusting the lamb to the tiger. We know what would happen in such a situation. Hence, we must insist on an international conference based on UN resolutions and the ruling of the International Court of Justice at the Hague.
"I represent the silent majority which is thirsty for ending this shocking subservience to Israel"
independent Palestinian presidential candidate
The World Court ruled earlier this year that all Palestinian territories seized by Israel in 1967, including East Jerusalem, were occupied territories and that all Jewish settlements built since were illegal and ought to be dismantled.
The court also ruled that the gigantic wall Israel is building in the occupied West Bank was illegal and illegitimate and ought to be torn down.
The choice is between concession
and surrender, says al-Barghuthi
Al-Barghuthi said the first decree he would issue if elected president would be the dismantling of the Palestinian Legislative Council, which he said was no longer legitimate since it had outlived its usefulness and term of office.
His statements came as the Palestinian election campaign officially got under way and the leading candidates sought to sell their programmes to a politically conscious electorate.
According to the latest opinion polls, Abbas remains the favourite, with 43% of respondents saying they will vote for him on 9 January.
However, al-Barghuthi's campaign seems to be steadily gaining momentum, with nearly 18% of respondents saying they support him.
Palestinian political analyst Hani al-Masri told Aljazeera.net on Saturday that al-Barghuthi could pose a serious challenge to Abbas if the main Palestinian Islamic movements decided to support him.
"I think Dr Mustafa will become a real challenge to Abu Mazin [Abbas] if Hamas and the Islamic Jihad support him," he said.
Hamas and its junior sister movement, the Islamic Jihad, have decided to boycott the presidential elections.