Kaddoumi, a long-time rival of Abbas and one of the founders of the Fatah movement, claimed he had transcripts of the Palestinian president discussing the issue with Ariel Sharon, the former Israeli prime minister.
The Palestinian Information ministry described the allegations as untrue and accused Al Jazeera of "devoting significant segments of its broadcasts to incitement against the Palestinian Liberation Organisation and the Palestinian Authority".
The ministry said it was taking the network to court for airing Kaddoumi's statements.
The accusations were rejected by Al Jazeera which defended its "professional journalistic standards", criticising the PA's repression of press freedoms and its apparent refusal to tolerate the opinions of others.
In a statement released at its Doha headquarters on Wednesday, Al Jazeera said it was "stunned" that it had been sanctioned for the story, which had also been aired by several other media.
A prominent human rights group and a media watchdog also condemned the PA's suspenion of Al Jazeera's operations in the occupied West Bank.
New York-based Human Rights Watch (HRW) on Friday called on Palestinian officials to immediately allow the network to reopen its offices in Ramallah.
"The suspension of Al Jazeera sends a clear message that the Palestinian Authority has red lines when it comes to free speech," said Sarah Leah Whitson, the Middle East and North Africa director at HRW.
The Brussels-based International Federation of Journalists (IFJ) also criticised the suspension, calling it "a serious violation of press freedom".
"It shows intolerance on the part of the Palestinian Authority and suggests that it is trying to control [the] media by suppressing reporting which it does not like," Aidan White, the general-secretary of IFJ, said in a statement.
"The ban should be lifted immediately."
The Foreign Press Association in Jerusalem, which groups international news organisations in Israel and the Palestinian territories, said it was "deeply concerned" by the PA's move.
"We urge the PA to reconsider and are urgently seeking a resolution in line with the PA's stated commitment to freedom of the press," it said.