Looks like Yasser is back in charge, ah well back to sleep
Mr Abbas - also known as Abu Mazen - offered to stand down before beginning a closed-door meeting with MPs in the West Bank town of Ramallah.
Palestinian officials denied earlier reports that Mr Arafat had already accepted the resignation, saying the Palestinian leader was still considering it.
The BBC’s Richard Miron, in Jerusalem, says that, if Mahmoud Abbas’s resignation is accepted, it will mark a severe crisis for the Palestinians and leave them diplomatically isolated.
Yasser Arafat will be left in charge and, for both Washington and Ariel Sharon’s government, that is unacceptable.
Israel said it was monitoring the developments, but would not accept “control over the Palestinian Authority [reverting] back to Yasser Arafat or one of his loyalists”.
British Foreign Secretary Jack Straw said the situation had “grave” implications for the peace process.
“It is a further difficulty, a huge tragedy, that the Palestinians should be so divided,” Mr Straw said.
Last Sunday, US envoy John Wolf reportedly warned Palestinian officials that Washington would “not allow the fall of the Abbas government”.
Credibility ‘undermined’
In submitting his resignation, Mr Abbas may be hoping Mr Arafat will bow to international pressure and bring him back - or bring in another prime minister with more authority.
Mr Arafat has refused to hand over crucial powers to Mr Abbas, limiting his ability to control militant violence and doing nothing to bolster his standing among ordinary Palestinians.
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The breakdown of the American-led peace plan has precipitated this crisis.
Mahmoud Abbas has staked his credibility on its success and the renewed violence has undermined his position, our correspondent adds.
Palestinian legislator Hanan Ashrawi said the way forward should not concentrate on “power struggles” but on “how to build a system of government that will empower Palestinians to deal with external challenges”.
‘Tainted by terrorism’
In a speech to MPs reviewing his first 100 days in office on Thursday, Mr Abbas publicly admitted rifts with the Palestinian leader.
“Either provide the possibility of strong support for carrying out [the mandate] or you can take it back,” he said.
Mr Arafat still largely controls the Palestinian Authority’s security services and Mr Abbas wanted that control transferred to him so that he could tackle militant groups.
Mr Abbas was appointed prime minister after the US refused to deal with Mr Arafat, describing him as a leader “tainted by terrorism”.
Meanwhile, European Union foreign ministers agreed on Saturday to take the first step towards outlawing the political wing of Hamas as a terrorist organisation, diplomats said.
Ministers - meeting in the Italian resort of Lake Garda - had agreed to ask a group of intelligence services from all 25 EU members and future member states to examine the militant group and make recommendations.
Commenting on the latest political crisis, the EU expressed deep concern at the “serious risk of dangerous instability” at the head of the Palestinian leadership.
The EU, along with the US, the UN and Russia makes up the “quartet” of mediators in the Middle East peace process. Plans have been announced to bring the four parties together for a meeting on 22 September.