The bereaved parents of the TV journalist, who was shot dead more than 10 years ago, had knocked the door of the chief minister, seeking speedy trial and justice for her.
The chief minister has taken a strong note of the Vishwanathan case, a senior government official said.
"He (Kejriwal) has also directed Chief Secretary Vijay Dev to issue show cause notice to the public prosecutors who missed the hearings," the official said.
The chief minister has said it is shocking to hear that they missed hearings.
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Kejriwal has also directed to appoint a good special public prosecutor in consultation with the Home Ministry immediately, he added.
In a letter to the CM, Soumya's father, M K Vishwanathan, had written that he and his family were tired of the "hollow assurances" from authorities, and expressed hope from a "concrete response" from him.
Five people were arrested in 2009 on the charges of murder and are presently in custody. The trial in the case is going on in the Delhi's Saket district court for the last 10 years.
"We are seriously concerned about both, the pace at which the trial is moving as well as the quality of efforts being put in the proceedings by the prosecution.
"Hollow assurances from authorities have tired us out and we sincerely hope for a concrete response from you at the earliest," her father said.
He said the recent change in the "public prosecutor has raised our concerns as he, once again, was absent from the court on the date of the last hearing (Feb 2)".
Unlike the first prosecutor on the case, the current and the previous public prosecutors have been "unresponsive" in giving any updates to his family on the progress in the case, M K Vishwanathan said.
With inputs from PTI
