In California, the suspect's father called on the gunman to surrender, as did relatives of one of the victims in New Jersey.
Pallipurath is accused of killing James, who prosecutors say had taken out a restraining order against him. Authorities say he also fatally shot Dennis John Mallosseril, who maintained the church's Web site and who tried to break up the rampage.
James' cousin, Silvy Perincheril, was in "extremely critical condition," Passaic County Prosecutor James Avigliano said.
The shooting occurred inside St. Thomas Syrian Orthodox Knanaya Church in Clifton, a small community about 17 miles west of Manhattan. Members of the church are mostly first generation immigrants and their children from Kerala.
All three victims were shot once in the head, and never regained consciousness, depriving investigators of the opportunity to interview them. James died at 3:30 p.m. Sunday and Mallosseril died three hours later.
Pallipurath fled in a green 2004 Jeep with California license plates and a black soft top. The search was centering on Georgia, where the suspect has relatives.
"We'll catch him," Avigliano said. "He needs to give himself up before we catch him."
Pallipurath is accused of opening fire Sunday just as the congregation was finishing its prayers for the dead, a staple of weekly worship service. Authorities say the gunman fired more than three times, but that only three people were hit. No one else was injured.
After fleeing three months ago from what relatives said was an abusive, arranged marriage in California, James came to New Jersey and stayed with Perincheril, her cousin who lives in Hawthorne.
"She found out he wasn't all he was cut out to be," Avigliano said. "He was abusive toward her, and she left him and came out here."
The couple were married just over a year ago in India and moved to Sacramento in January.
Reshma's aunt, Maria Joseph, of Hartford, Conn., said she warned her niece, who was studying to become a nurse, not to marry him. Other relatives told her the man had a history of "behavioral problems," Joseph said.
Mathai Pallipurath, the suspect's father, told The Associated Press Monday he didn't know his son's whereabouts and hadn't heard from him. But he urged his son to surrender, and asked his son's friends to do the same if they hear from him.
He said he thought his son and daughter-in-law were happy together, and described his son as "handsome" and "a nice guy."
According to a published report, however, the elder Pallipurath was granted a restraining order against his son in May. The father said Joseph was abusive to family members and had threatened his life.
In the story posted on its Web site Monday, The Sacramento Bee, citing family court records, said the restraining order was dropped at Mathai Pallipurath's request on June 17. A man who answered the phone at the family's Sacramento home Monday evening said Mathai Pallipurath did not wish to speak to a reporter.
Jacob Abraham, Mallosseril's cousin, called on Joseph Pallipurath to stop running and face his punishment.
"Turn yourself in," Abraham said outside the church Monday, after traveling from Houston to be with his grieving family. "He has to get his punishment, whether it's from the justice system or from God."
The parish priest, Rev. Thomas Abraham, who is not related to the victim's cousin, said he heard a loud noise, and thought something had fallen in the church. He got up to go toward the noise, only to be hit with a wave of parishioners pushing him backward, saying someone was shooting inside the sanctuary.
He said church members are in shock.
"They're all scared; they're all really upset," he said. "We have to hold together in this time of adversity."
In India, Archbishop Kuriakose Mar Severios, who is based in Kerala, was planning to travel to New Jersey to mourn with the congregation on Wednesday.
Associated Press writers Wayne Parry in Atlantic City, Bonny Ghosh in Clifton and Judy Lin in Sacramento, Calif., contributed to this story.