Mr Streeting is expected to use the publication of new NHS waiting list data on Thursday to argue that he has a strong record of government delivery.
He will then give a speech on Saturday at an event organised by Progress, a Blairite pressure group, to lay out his credentials to be prime minister.
Sir Keir held last-ditch talks with MPs and ministers in Parliament on Wednesday night, urging them to reject a leadership contest that would cause “chaos”.
It is understood Sir Keir told would-be rebels that a race for No 10 would paralyse the Government.
He insisted he would stand against any rival but said any contest “would destroy our country and our party” and that Labour would not be forgiven if MPs “plunged the country into chaos”.
Cabinet ministers told MPs in the tearoom that “a leadership contest is not what the country wants or what the country needs right now”, one source said.
They told MPs that Sir Keir was “ready to fight” and that “the country gave us a massive message last week, and it wasn’t to descend into chaos.”
The news that Mr Streeting was planning to resign came as the King prepared to give his address to MPs and peers at the State Opening of Parliament, where he announced 37 bills for the new parliamentary session.
Mr Streeting’s team had previously promised not to release details of his meeting with the Prime Minister for fear of overshadowing the King’s Speech.
Allies of Sir Keir complained that his leadership manoeuvring had become a snub to the King and had damaged the Prime Minister’s attempted “reset”.