The man suspected of killing at least 26 people in a Baptist church in a rural Texas had a "connection" to the establishment and the massacre was not a random act, the state's governor has said.

Greg Abbott told ABC's Good Morning America he expected people to learn about any such link "in a few days."

He said he didn't want to go further, saying "law enforcement is looking very aggressively into this."

"I don't think this was just a random act of violence," Mr Abbott told anchor George Stephanopoulos.

But when pressed to elaborate on his connection theory, the governor replied to say "it's very important that law enforcement have the ability... to tie the loose ends of this investigation up."

He called the man, identified by US media as Devin Patrick Kelley, "a very deranged individual."

Relatives of the gunman sometimes worshipped at the church where he opened fire, but were not there during Sunday's attack, Wilson County Sheriff Joe Tackitt Jr said.

"We know that his ex-in-laws or in-laws came to church here from time to time," Mr Tackitt Jr told CNN in an interview.

"They were not here yesterday."

Dressed in black tactical-style gear and armed with an assault rifle, the gunman opened fire inside a small Texas church, killing 26 people ranging in age from five to 72 years old.

He later died of a self-inflicted gunshot wound, Mr Tackitt said.

He said gunfire was exchanged between the gunman and two armed citizens during a vehicle chase after the shootings.

"There was some gunfire exchanged, I believe, on the roadway also, and then [the shooter's vehicle] wrecked out," said Mr Tackitt.

"At this time we believe that he had a self-inflicted gunshot wound, after he wrecked out."