"We will absolutely want him to have the death penalty," Nikki Haley told NBC television.
Suspect Dylann Roof, 21, is due to make his first court appearance on Friday.
He was arrested on Thursday more than 200 miles away in North Carolina and flown back to South Carolina.
Police are treating the killings at the Emanuel AME Church on Wednesday evening as a hate crime.
Prayer vigils have been held in churches in Charleston and across the US for the six women and three men who died.
At the vigil for victim Sharonda Singleton, her teenage children told the BBC they had forgiven her killer and wanted to focus on moving on in a positive way.
"We already forgive him for what he's done," said her son, Chris.
"And there's nothing but love from our side of the family. Love is stronger than hate."
Churches in Charleston were full to overflowing on Thursday evening as prayer services were held. Some services were held outdoors.
Hundreds gathered outside the Emanuel AME Church to pay tribute.
Governor Haley told NBC's Today show that South Carolina had been "hurt" by the deaths of nine innocent people.
She said she wanted the suspect tried on state charges in South Carolina rather than federal charges.
Mr Roof is due to appear in court via video link for a bail hearing on Friday. He is being held at a detention centre in the Charleston area, the county sheriff's office said.
He was detained on Thursday after police acting on a tip-off stopped his car in Shelby, North Carolina.
Police had earlier released CCTV images of the suspect and the dark saloon car he had driven away in.
Mr Roof's social media presence suggests he was interested in white supremacy.
His Facebook profile page shows a picture of him wearing a jacket with flag-patches from apartheid-era South Africa and Rhodesia - the name of Zimbabwe during the era of white minority rule. He also had a Confederate flag plate on his car.
Dalton Tyler, who said he was a friend of Mr Roof, told ABC News the suspect had spoken in support of racial segregation and had said "he wanted to start a civil war".
It emerged on Thursday that the gunman had sat in a Bible study group at the church for nearly an hour before launching his attack.
In pictures: Americans share images of racial imbalance after Charleston
"The suspect entered the group and was accepted by them, as they believed that he wanted to join them in this Bible study," Charleston County Coroner Rae Wilson said.
She said he then became "very aggressive and violent".
Eight people died at the scene and one person died later in hospital. There were three survivors.
The victims were named as Pastor Clementa Pinckney, 41; Cynthia Hurd, 54; Tywanza Sanders, 26; Ms Singleton, 45; Myra Thompson, 59; Ethel Lance, 70; Susie Jackson, 87; the Rev Daniel Simmons Sr, 74; and DePayne Doctor.
Cynthia Taylor, a niece of Ms Jackson, said she had spoken to a survivor, Felecia Sanders, who said she had played dead as she lay on top of her granddaughter to protect her.
US President Barack Obama said the killings again raised the issue of US gun ownership, saying: "At some point, we as a country have to reckon with the fact that this type of massacre does not happen in other advanced countries".
The Emanuel church is the oldest African Methodist Episcopal (AME) church in the US south. Civil rights leader Martin Luther King gave a speech there in April 1962.
Tensions have been heightened since the shooting two months ago of Walter Scott, an unarmed black man by a white police officer in North Charleston, which prompted angry protests.
The officer has since been charged with murder.
The man suspected of shooting dead nine people at an African-American church in Charleston should face the death penalty if convicted, South Carolina's governor has said.