Palestinian officials say their leader Yasser Arafat has accepted the resignation of Prime Minister Mahmoud Abbas - but it is not clear if the decision is final.
Arafat: Resisting US and Israeli pressure to transfer power
Mr Abbas - also known as Abu Mazen - made his offer to stand down on Saturday following a power struggle with Mr Arafat over control of Palestinian security forces.
Mr Abbas has a few weeks left as caretaker prime minister while Mr Arafat finds a replacement - and Mr Abbas could in theory still head a new government, the BBC's Richard Miron reports from the West Bank town of Ramallah.
The political turmoil has fuelled international concern for the fragile peace process, with the White House stressing that it remains committed to the peace plan known as the roadmap.
A US administration spokesman said that "at this critical moment, it is important that all parties consider carefully the consequences of their actions".
In Ramallah earlier Mr Arafat "accepted the prime minister's resignation" at a gathering of more than 80 Palestinian MPs, according to one of those present, Mohammed Hourani.
"Today, we lost an honest prime minister who only wanted to serve his people," he added.
However, Labour Minister Ghassan al-Khatib told Reuters news agency that no final decision had been announced by Mr Arafat.
Mr Abbas was appointed less than four months ago, under international pressure for reform within the Palestinian Authority to try to end the cycle of Palestinian-Israeli violence.
Cycle of violence
The fragility of the peace plan was underlined on Saturday when the founder and spiritual leader of the militant Hamas movement, Sheikh Ahmed Yassin, narrowly escaped an Israeli air strike on Gaza City.
The Palestinians' political disarray combined with this attack has left the roadmap in a critical condition, our correspondent says.
Palestinian Foreign Minister Nabil Shaath told the BBC that the situation was very serious. "We need a third party to step in", he said.
For the US and Israel, Mr Abbas has represented the acceptable face of the Palestinian leadership.
Israel said it was monitoring developments, but would not accept "control over the Palestinian Authority [reverting] back to Yasser Arafat or one of his loyalists".
US Homeland Security chief Tom Ridge said Mr Abbas had been consistently undermined by elements within the Palestinian Authority, and his departure would delay efforts to get the two sides back to negotiations.
UK 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," he said.
Wrangling between Arafat and Abbas has helped stall the roadmap
The European Union is sending its foreign policy chief, Javier Solana, to Cairo immediately to discuss the Palestinian crisis with Arab officials.
The EU, along with the US, the UN and Russia makes up the "quartet" of mediators in the Middle East peace process.
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.
The prime minister has staked his credibility on successful peace efforts, and the renewed violence has undermined his position, our correspondent says.
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 Abbas was appointed prime minister after the US refused to deal with Mr Arafat, describing him as a leader "tainted by terrorism".
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.