A woman with a rifle has been killed by two off-duty police officers after entering one of the US’s biggest evangelical churches and opening fire.

Police said a young child with the woman was critically injured and another man nearby was wounded.

Houston Police Chief Troy Finner said the woman in her early 30s entered the Houston megachurch of Joel Osteen with a long gun and a backpack shortly before 2pm local time on Sunday, accompanied by a child aged about five.

Two off-duty officers killed the shooter before she could kill anyone inside the church, which was preparing to host a Spanish-language service, Finner said.

The child was taken to Texas Children’s Hospital and was in a critical condition, he said. A man in his 50s sustained a non-critical leg injury and was also being treated at a local hospital.

The shooting happened between services at the megachurch, which is regularly attended by 45,000 people every week, according to the Hartford Institute for Religion Research. Osteen’s televised sermons reach about 100 countries.

“She had a long gun, and it could have been a lot worse,” Finner said.

The woman had threatened that she had a bomb, prompting authorities to search her backpack and vehicle, he said. They found no explosives.

“Our hearts are with those impacted by today’s tragic shooting and the entire Lakewood Church community in Houston. Places of worship are sacred,” Texas Governor Greg Abbott said.

“We’re devastated,” Osteen said, adding he would pray for the victims and their families.

“We don’t understand why these things happen, but God’s in control. We’re going to stay strong. We’re going to continue to move forward.”

The Lakewood Church, which seats 16,000 people, is led by celebrity pastor Osteen and his wife and co-pastor Victoria Osteen.

Osteen is one of the wealthiest and most popular pastors and prosperity gospel preachers in the US. According to the church’s website, Osteen’s media broadcasts, podcasts and radio programming reach millions of US households and audiences worldwide.

The Houston church is located in the former sports arena for the Houston Rockets of the National Basketball Association.