The official, who asked not to be named, said Abbas had earlier on Tuesday submitted his resignation to Palestinian leader Yasser Arafat, who heads Fatah.
Abbas, who helped co-found Fatah four decades ago, was to have met Israeli Prime Minister Ariel Sharon on Wednesday but scrapped the meeting, sparking a new crisis in the Middle East peace process, hours after a fatal bomb attack.
Abbas tendered his resignation to Fatah after fellow members expressed unhappiness over his negotiating strategy with Israel over the US-backed roadmap.
Serious disagreements emerged during the Fatah Central Committee meeting on Monday night, a senior Palestinian official said.
“Some members lashed out at Abbas’s performance in contacts with Sharon so far and asked him to resign from the committee,” the official said.
The heated argument turned into shouting between Abbas and some of his colleagues in the committee.
The Prime Minister then sent two letters to Arafat, one of them offering his resignation from the central committee.
In the other letter, he asked Arafat and Fatah to send him their instructions on how to run his government and negotiations with Israel.
“If he rejects their ideas, he will resign as prime minister,” the official said.
Sources close to Abbas said he had pulled out of the summit scheduled for Wednesday in protest against the Israeli government's decision to release only 350 prisoners. It amounts to five percent of the total Palestinian prisoners in Israeli jails.
But a Palestinian official said Abbas had called off his meeting with Sharon following the bomb attack near Tel Aviv.
There was confusion over who was responsible for the attack which is threatening to jeopardise the ceasefire in the region.
The Jenin branch of the Islamic Jihad claimed responsibility for the explosion, which killed a woman and an alleged bomber. But its central leadership issued a counter-denial.
The Jenin branch distributed the picture of a young man, Ahmad Yahya, 22, who it said carried out the operation.
But Abd Allah Al-Shami, a political leader in the group, told Aljazeera he had not received any confirmation that al-Quds Brigades were behind the operation. The Brigades is the military wing of the Islamic Jihad.
Yahya queered the pitch
for the peace process
Al-Shamisaid the Islamic Jihad usually issued official statements to claim responsibility for such operations.
Israel said the blast proved that the truce was worthless and highlighted the need for a crackdown by Palestinian authorities.
"The 'hudna' which they signed is not worth the paper its written on," said Raanan Gissin, spokesman for Israeli Prime Minister Ariel Sharon, using the Arabic word for a temporary truce.
The interim truce and Wednesday’s cancelled meeting between Abbas and Sharon are part of the overall peace process between Palestine and Israel drawn by the Quartet – Russia, United States, United Nations and European Union.