The 35-year-old actress told how Andrews, who started in the original 1964 film, was “excited” for Blunt to take on the role.
She told Variety: ''I met her years ago at some event. And she was so charming and so lovely. Little did I know that years later I would be off playing Mary Poppins.
“But [director] Rob [Marshall] was very close with her, she was incredibly supportive of me playing the part and excited for me to do it.”
Blunt also revealed that Andrews chose not to appear in the reboot because she didn’t want to discredit the star.
She added: “There was discussion about [how] maybe she would come and do a bit in the movie.
“She said to Rob, 'This is Emily's version of her, and I don't want it to be that she's playing Mary Poppins the whole way through, but then I come in like, Oh, but there's the real Mary Poppins’.”
Blunt, who plays the loveable magic nanny from the hit Disney classic, looked stunning in a billowing white dress as she worked the red carpet hand-in-hand with husband Krasinski.
The pair couldn’t stop smiling as they posed affectionately for the cameras at the star-studded Hollywood bash.
Blunt was also joined by legendary actor Dick Van Dyke who is the only actor from the original 1964 musical to feature in the new film.