It was the first meeting between the two after Abbas threatened to quit as prime minister last week and resigned from Fatah’s policymaking committee that is headed by Arafat.
“President Arafat and Mahmoud Abbas settled their differences during their meeting,” said an official, who spoke on condition of anonymity.
They have adopted a “formula on the ways and means of conducting future negotiations (with Israel) as well as over security matters,” the official said.
Details on the agreement were not disclosed, but the official said that both leaders would avoid appearing in a quarrel in the future.
The meeting was held at Arafat’s headquarters in the West Bank city of Ramallah.
As the two leaders began talks, an official at Abbas’ office said that the prime minister would “reiterate that Arafat is still the president even if there are internal disputes".
"The prime minister would never abandon Arafat," the official said.
Colleagues of Abbas in Fatah have expressed their dismay over his handling of talks with Israel and accused him of being too soft.
Abbas, who lacks public support among Palestinians, came to power in May after massive US pressure on Arafat to appoint him as prime minister.
He is favoured by both Israel and the United States as part of a policy to marginalise Arafat.
Britain disagrees with Sharon
Israeli Prime Minister Ariel Sharon also stepped up his campaign to isolate Arafat, demanding European countries he is visiting to cut ties with the elected Palestinian president.
Sharon (L) wants Blair (R) to
However, Sharon appeared to have failed to convince British Foreign Secretary Jack Straw whom he met on Monday in London.
"(Straw) made it clear that the British position, which is also that of the European Union, is that we would continue to have dealings with Arafat," a British official said after Straw held talks with Sharon.
Sharon later met British Prime Minister Tony Blair, who was expected to press the Israeli prime minister to continue removing "rogue" Jewish settlements - those not approved by the Israeli government - erected on Palestinian territories.
All Jewish settlements set up in the West Bank and Gaza Strip are illegal under international law.
After his three-day-visit to Britain, Sharon will head to Norway.
Israeli officials have hailed the trip as a sign that European opposition to Sharon has tempered in the wake of the “road map” plan sponsored by the United States, the European Union, the United Nations and Russia.