It comes after he was forced to cancel events when his mother-in-law was admitted to hospital following an accident.
The shadow Brexit secretary thanked people for their "support and kindness" in what he said had been - and would continue to be - a "very difficult time".
Sir Keir, who is a frontrunner in the race to replace Jeremy Corbyn, pulled out of events on Thursday, Friday and over the weekend as a result of his mother-in-law's condition.
Words cannot express our thanks for everything our incredible NHS are doing. I hope to be able to return to the leadership campaign on Monday.
— Keir Starmer (@Keir_Starmer)
She remains in a critical condition in hospital, it is understood.
The frontbencher wrote on Twitter on Saturday evening: "Heartfelt thanks to everyone in the Labour Party, especially the other leadership candidates, and to everyone beyond the Labour Party for the support and kindness you have extended to my family and me in what has been - and sadly will continue to be - a very difficult time.
"Words cannot express our thanks for everything our incredible NHS are doing.
"I hope to be able to return to the leadership campaign on Monday."
Planned leadership hustings in Leeds on Saturday were cancelled to ensure fairness to all the candidates after Sir Keir pulled out.