Asked about her remarks, Sir Keir said he was "really proud" to have appointed the UK's first ever female chancellor.
"I strongly believe that women in public life get much more criticism and abuse than men," he said, adding: "In politics, but it's also across a number of other areas. I'd also say the media frankly. And I think we need to acknowledge that."
The PM also said he would "absolutely" like to welcome the former Deputy Prime Minister Angela Rayner back into government at some point.
Rayner, who was housing secretary as well as Sir Keir's deputy, resigned in September after failing to pay enough tax when she bought a flat in Hove in East Sussex.
Twice referring to her as "Ange," he told reporters: "I'm friends with Ange and I like Ange a lot and we talk a lot. We still do. It's always good to have Angela."
"I've always said I want Angela back. Even back in September, at the time, I said she is going to be a big voice in the Labour movement," he said.
"But do I want Angela back at some stage? Yes absolutely."
He added: "I think she is the best example ever in the United Kingdom of social mobility - going from a pretty challenging childhood to being deputy prime minister of the United Kingdom.
"She is the story of social mobility above all other stories."
In an interview last weekend, Rayner did not rule out a return to frontline politics, telling the Daily Mirror she had not "gone away".
