And defines "serious" as: "Vital signs may be unstable and not within normal limits".
Scalise was wounded when a gunman opened fire at a GOP lawmaker baseball practice Wednesday morning.
Rep. Steve Scalise was shot June 14, 2017 in Alexandria, Virginia, a House colleague told CNN, in what sources are calling an apparent "deliberate attack".
One of the Capitol Police officers injured in Wednesday's shooting has thrown out the first pitch at the Congressional baseball game - to thunderous applause.
"He is more responsive, and is speaking with his loved ones", the hospital said in the statement.
Doctors "fully expect him to walk", Sava said, "and hopefully run". "I think that his risk of death right now is substantially lower than when he came in. he was as critical as you can be when he came in".
Sava said that multiple teams have worked on the congressman, with a combination of surgeries and procedures.
"After he leaves the hospital he will require a period of healing and stabilization", he said. Hundreds of bullet fragments remain in his body.
"There is more risk involved in removing them".
Investigators said in a statement that the Federal Bureau of Investigation has searched the van, which was parked not far from the Alexandria, Virginia, baseball field where Wednesday's shooting took place.
He did say an "excellent recovery is a good possibility".
Vice President Pence on Thursday visited House Majority Whip Steve Scalise (R-La.) in a Washington hospital, where he is recovering from a gunshot wound.
Medstar Washington Hospital Centre released the update on behalf of the Scalise family. He also received an additional procedure that day to stop bleeding.
Hospital officials said it is hard to predict how long the congressman will be in the hospital, but that he is expected to be able to walk and hopefully run after a period of rehabilitation.
Scalise's Chief of Staff shared a message from the congressman's family at a Friday press conference. He said doctors have turned down Scalise's sedation levels enough that the lawmaker has been able to respond to family members visiting him in the hospital.