Hungary's theatre chief offered to resign after a balcony fall injured two actors in his Romeo and Juliet production.
Júlia Szász played Juliet and Otto Lajos Horváth performed as her father Capulet during Friday's accident.
The pair are in a serious but stable condition in hospital.
National Theatre director Attila Vidnyánszky offered to quit on Monday, but it was rejected by Hungary's culture minister - János Csák.
Paramedics treated the pair after they fell behind the scenery from an elevated platform during the second act of the performance in Budapest.
They both later underwent surgery.
An investigation was launched, and Mr Csák said he would await its findings before taking further action. It is unclear when it might conclude.
Mr Vidnyánszky has served in his role as director of the National Theatre for 10 years and is a close ally of Prime Minister Viktor Orban.
His appointment was set to conclude in 2023, but it was extended another five years to 2028 earlier this year.
Mr Csák and Mr Vidnyánszky visited the Budapest hospital where the actors are being treated and met doctors.
In an Instagram post, Mr Csák said that the two actors' conditions were improving and wished them a speedy recovery.
Szász was scheduled to appear in National Theatre performances of John the Valiant and Woyzeck later this month.
She's also featured in a number of high-profile Hungarian film productions.
Horváth first gained success in the early 2000s as an actor and is known for performing in Hungarian films and television shows.
William Shakespeare's 1594 tragedy Romeo and Juliet tells the story of two Italian teenagers from feuding families who fall in love.
The pair share an intimate moment on a balcony and plan a secret marriage.