"Perhaps Robin Williams' greatest gift to us, if we choose to accept it, is a focused determination to help those with brain illness and finally take real action to stop the loss of one more precious life," Murphy (R-Pa.) said in a statement.
Law enforcement officials on Tuesday said the late actor committed suicide, though the final determination will be made by a coroner in Marin County, Calif., where the actor lived.
The actor’s death has put a spotlight on mental illness and prompted conversations about rising rates of suicide around the country.
Murphy wrote legislation at the behest of GOP leaders to overhaul the mental health system in response to the 2012 elementary school shooting in Newtown, Conn.
The measure has proven too controversial to move in one piece, though Murphy is keeping up the pressure.
House Republican leaders indicated in June that they would move some provisions individually, but Murphy argues that leaving out key components makes the reform effort unserious.
His bill would loosen standards for involuntary mental health treatment, increase psychiatric beds and gut the Substance Abuse and Mental Health Services Administration, which critics say does not help people who are seriously ill.
A range of powerful outside groups are uneasy about these reforms, leading to the wider stalemate.
A spokeswoman for the House Energy and Commerce Committee expressed hope that some portions of the bill would move in September.
Murphy, a psychologist, said mental health problems have become a “national crisis that demands our response.”
“There are nearly 40,000 suicides each year. Over the last decade the annual suicide rate among Mr. Williams' age group has increased nearly 30 percent. In what other discipline of medicine would we ignore such staggering statistics?”