Barghouti, 45, an extremely popular member of the young guard of Fatah, had told associated he planned to challenge Abbas, 69, in the election to succeed Yasser Arafat, who died Nov. 11.
Palestinian Cabinet Minister Kadoura Fares traveled to an Israeli jail in the city of Beersheba on Friday to meet with Barghouti armed with an appeal from Abbas to abandon his campaign.
Fares told a news conference Friday evening that Barghouti appreciated Abbas' gestures, including a promise to hold long-overdue elections in Fatah next year, and would support his candidacy.
"After a meeting of four hours, during which we debated this issue, Marwan Barghouti sends this message to the Palestinian people and its fighters ... He calls on the members of the movement to support the movement's candidate, Mahmoud Abbas," Fares said.
While the two men met, word came that Fatah had set Aug. 4, 2005, as the date for an internal election.
The young leaders of Fatah have complained that they have been frozen out of the top leadership positions in the party by older officials scared of losing power. Fatah has not held a general conference to elect a new leadership since a 1989 gathering in Algeria.
But the Fatah Revolutionary Council decided Friday to hold a general conference Aug. 4, Yasser Arafat's birthday, to elect new party leaders, according to Amin Maqboul, a senior Fatah official.
The elections should have been held every five years. The party conference will probably be held abroad to allow Fatah officials in Lebanon, Jordan and other countries to participate, Maqboul said.
Maqboul said the general conference "will give the new young generation a better role to play in the leadership."
Israel, meanwhile, agreed to remove all roadblocks in the West Bank on Jan. 9, the day of the presidential election, according to security officials speaking on condition of anonymity. Israel has said it will do its utmost to ensure that voting goes smoothly.
Barghouti is serving five life terms in an Israeli jail after being convicted of murder. Israel says Barghouti, 45, was involved in attacks that killed four Israelis and a Greek monk. Barghouti has denied involvement.
His supporters have said they are counting on international pressure on Israel to free him. Israel's leaders insist Barghouti will remain in prison.