Frank Pomeroy told leaders of the Southern Baptist Convention earlier this week that it would be too painful to continue using First Baptist Church as a place of worship.
A national Southern Baptist spokesman said Mr Pomeroy discussed the plan with the denomination's top executives, who travelled to the rural community in a show of support.
Sing Oldham said the pastor described the building as "too stark of a reminder" of the massacre. Mr Pomeroy expressed hope he could turn the site into a memorial for the dead and put up a new building on property the church owns.
On Wednesday, Vice President Mike Pence joined Texas Governor Greg Abbott at a memorial service for the victims of the gunman.
Mr Pence told the crowd that the attack was the worst mass shooting at a church in American history and called the gunman "deranged".
"Whatever animated the evil that descended on that small church, if the attacker's desire was to silence their testimony of faith, they failed," the vice president added.
The governor said Texans come together at times of crisis and tragedy. "It's what we do," Mr Abbott said. People in the crowd responded "amen".
He also proclaimed Sunday November 12 a state-wide day of prayer.
Mr Pence also visited wounded congregants at a San Antonio hospital and met with families of the dead in Floresville, not far from Sutherland Springs. He went from table to table at a high school library, attempting to console devastated family members.
"The whole country is praying over you," he told one man who lost his sister-in-law.
He stopped to talk with John Holcombe, whose family was decimated by the shooting. Mr Holcombe, who suffered shrapnel wounds, lost his wife, Crystal, who was pregnant with their first child. Also killed were three of her children, his parents, a brother and a toddler niece.
Earlier on Wednesday, Mr Pence said President Donald Trump had ordered federal agencies to provide extensive help to the investigation, including 100 on-site FBI agents.
The Texas Department of Public Safety released an official list of those killed in the rampage. The eight male victims and 17 female victims ranged in age from one to 77.
Eight of the fatalities were children or teenagers. The oldest of them was 16.
Authorities said the 26 dead also included Crystal Holcombe's unborn baby. All the victims died at the scene, except for one child who died in hospital.
Eleven people remained hospitalised with wounds they suffered in the attack.
Associated Press via Press Association