Michael Smith, 55, was a veteran officer who was once selected by the Dallas Police Association for the Cops' Cop award.
His priest, Fr Michael Forge, from Mary Immaculate Catholic Church, notified parishioners of Mr Smith's death in an email.
Mr Smith, his wife Heidi and their two daughters were part of the parish in Farmers Branch, north of Dallas.
"As you may have heard by now officer Mike Smith, husband of fourth grade teacher Heidi Smith and father of Victoria (Class of 2016) and Caroline (incoming 4th grade) was shot and killed last night in Dallas while on duty," Father Michael wrote.
"I'm asking all of us to pull together in prayer and support for the Smith family, as well as the other officers' families who were killed along with Mike."
He was a volunteer at the YMCA and his church, and was involved in working with children at risk, and once developed a sports programme for youngsters at the local YMCA, friends said.
"He's just a really nice guy. He loved his wife, loved his daughters. He spent time with his family. The whole situation is really sad," Vanessa Smith, a friend of the officer's wife, said.
Meanwhile it's been revealed the Dallas gunman had been sent home from Afghanistan after being accused of sexually harassing a female, and was described as a loner who followed black militant groups on social media.
Micah Xavier Johnson, who fatally shot five officers and wounded seven more before police killed him with a remote-controlled bomb on Friday, lived with family members in the blue-collar suburb of Mesquite in Texas, where he played basketball for hours at a time.
Friends there said the 25-year-old black man did not seem interested in politics, but his Facebook page suggests otherwise: He "liked" black militant groups including the African American Defence League and the New Black Panther Party, which was founded in Dallas.
His photo showed him wearing a dashiki and raising his fist over the words Black Power, and his cover shot carried the red, black and green Pan-African flag.
When authorities searched Johnson's home on Friday they found bomb-making materials, ballistic vests, rifles, ammunition and a personal journal of combat tactics.
Dallas police chief David O Brown said Johnson told negotiators before he was killed that he was acting alone and was unaffiliated with any group.
The chief said Johnson cited the fatal shootings of black men by police officers in Louisiana and Minnesota, which prompted the protest march in Dallas and many other cities.
"The suspect said he was upset with white people and wanted to kill white people, especially white officers," Mr Brown said.
The other victims were Brent Thompson, Patrick Zamarripa, Michael Krol and Lorne Ahrens.
