BBC Newsnight revealed earlier this week that the party’s investigation was completed in December 2023.
Labour’s NEC issued her with a “formal warning” for “engaging in conduct that was in the opinion of the NEC, prejudicial and grossly detrimental to the Labour Party”.
It said it expected her to undertake an “online, e-learning module” which a source said was a two-hour antisemitism awareness course.
Ms Abbott did the module in February, after which it is understood she received an email from Labour’s chief whip acknowledging she had completed it.
However, as recently as Friday, Sir Keir had been saying the investigation into her comments was not “resolved”.
Prime Minister Rishi Sunak said Labour needed to “clear up” this issue.
“The Labour Party has been telling everybody this investigation into Diane Abbott is ongoing, it now appears it concluded months ago,” he said.
Meanwhile, Mr Corbyn, who was suspended as a Labour MP in 2020 for saying the scale of antisemitism within Labour’s ranks had been “dramatically overstated” by his opponents, has launched his campaign to stand as an independent candidate in Islington North.
Speaking at a launch event, he said he had been “disturbed at the way Diane’s been treated” and had sent her a “message of support”.
A complete list of candidates standing in the seat will be available on the BBC website after nominations close.