A police office has said that "Free Palestine" was written on the gun of the woman who opened fire at celebrity pastor Joel Osteen's Lakewood Church in Houston, according to US network ABC.

Sources told the website that investigators were trawling social media posts of the suspect, described as a woman between 30 and 35 years old.

Detectives believe the suspect fired as many as 12 shots in Sunday’s attack, ABC reports.

When the shooter entered the church, she was accompanied by a child aged 4 or 5, Houston police chief Troy Finner told ABC.

The suspect opened fire with a rifle, and two off-duty officers fired back, killing her, Finner said.

The child was also shot and has been hospitalized in critical condition, Finner said.

The shooting took place shortly before the church's 2 pm Spanish language service was set to begin.

Harris County Judge Lina Hidalgo said in a statement, "I will not make any assumptions because information continues to come in as to what motivated the shooter, but I am asking that the investigation look into whether it was a hate crime, given the shooting took place at an all-Spanish service.

"We all stand with the Lakewood congregation as they recover from this terrifying day and with the young child and adult who are known to have been hurt in the shooting," Hidalgo added.

"Our community is devastated by today's events and grateful for the swift actions of law enforcement," Osteen wrote on social media. "Please join me in continued prayer for healing and peace."