Palestinian Prime Minister Mahmoud Abbas has threatened to stand down, in a sign of rising tensions within the Palestinian leadership.
Arafat leads Fatah, which has signed a six-month truce
Mr Abbas - widely known as Abu Mazen - also tendered his resignation from the ruling body of Yasser Arafat's Fatah movement.
Both offers comes amid severe splits in the group over the release of Palestinian prisoners held in Israeli jails.
Abu Mazen - a moderate backed by the United States - has been facing strong pressure from Palestinian leaders seeking a tougher stance towards Israel.
He (Abbas) is saying to the Fatah members: 'If you think I am to be blamed, this is my resignation, and you can sort things out'
Saeb Erekat, senior Fatah member
The resignation moves follow a stormy meeting of Fatah's Central Committee in the West Bank town of Ramallah on Monday.
Palestinian officials accused the prime minister of making too many concessions to Israel, which has promised to release just a few hundred of the more than 6,000 prisoners it holds.
Afterwards, Abu Mazen sent two letters to Mr Arafat.
In one letter, he asked Fatah to instruct him on how to deal with Israel, saying he was ready to resign as prime minister if he disagreed with their suggestions.
In the other, he offered to resign from the Fatah leadership.
There is no indication that Mr Arafat has accepted either offer.
The move came just days after Israel said it would release more Palestinian prisoners, but that militants from the Hamas and Islamic Jihad groups would not be eligible.
The Israelis have urged Abu Mazen to crush the militant groups by force.
But the BBC's David Chazan in Jerusalem says that is something the prime minister has so far rejected, because he fears it could trigger a Palestinian civil war.
Abbas [L] has been pressing Israel to free more prisoners
Saeb Erekat, a senior Fatah member, told the BBC that Abu Mazen's offers reflected serious splits within the Palestinian leadership.
"I believe it's a genuine move by Mr Abbas. He's saying to the Fatah members: 'If you think I am to be blamed, this is my resignation, and you can sort things out,'" Mr Erekat said.
Mahmoud Abbas - alongside with Mr Arafat - was the co-founder of Fatah in 1965.
Fatah is one of three major Palestinian groups to have declared a truce in attacking Israelis.
The 29 June truce statement - by Hamas, Islamic Jihad and Fatah - calls for the release of "all Palestinian and Arab prisoners" and threatens a resumption of violence if the condition is not met.
The deepening rift comes amid reports that the US is planning to provide its first direct funding to the Palestinian Authority, in an apparent attempt to bolster Abu Mazen's position.
The Washington Post quotes unnamed US officials as saying the administration would initially make a $20 million contribution towards social services run by the PA.
In the past the US has provided only indirect aid to the Palestinians, notably through the United Nations and non-governmental organisations.
The Washington Post says the aim of the funding is to offer a counterweight to services provided by militant groups such as Hamas.
On Tuesday, Washington reaffirmed its support for Abu Mazen, praising his leadership in pursuing the Middle East peace plan, known as the roadmap.
"We stand behind Prime Minister Abbas... His efforts to end terror and violence have presented a real opportunity to move forward," State Department spokesman Philip Reeker said.