Joseph Pallipurath, a native of Kerala, who fatally shot his 24-year-old wife Reshma James, who wanted to end the "abusive marriage", and critically wounded a third person, admitted to Sunday's shooting after he surrendered peacefully at a motel near Atlanta on Monday, Georgia prosecutor Eric Crawford said.

The accused also agreed to return to New Jersey when he was produced in a court in Georgia.

Pallipurath also did not apologise express remorse for the crime he committed, Crawford was quoted as saying by media.

The accused told authorities that he believed that church members were blocking his attempts to contact his wife, Crawford said.

The couple had an arranged marriage just a year ago and Reshma had suffered abuse right from the initial days of her marriage in Kerala, which continued here, police said.

Reshma had left him about three months ago to stay with her cousin in New Jersey and obtained a restraining order against him.

Pallipurath had drove across US on Sunday from California to New Jersey, to persuade his wife Reshma to return to him and then shot her when she spurned him.

He was on run after the shooting in which another man Dennis John Mallosseril, 23, who maintained the church's website, was also killed when he attempted to intervene between the couple.

A third person, James' cousin, Silvy Perincheril, 47, who was shot in the head remains in critical condition. Meanwhile, Reshma's body is expected to be sent to India and officials at the Indian consulate in New York have offered all help to facilitate the process.

Police has also recovered the jeep in which Palliparuth escaped after the incident and the revolver which he is believed to have used during the shooting.

The accused is expected to be back in New Jersey within next eleven days to face the murder charges. He is charged with two counts of homicide, an attempted homicide and weapon offences.