By David Schwartz

PHOENIX (Reuters) - The family of a Border Patrol agent killed by gunfire near the Mexican border in Arizona described him on Thursday as a hero, recounting how he once carried a pregnant immigrant woman to safety after finding her in distress in a remote area with no shoes.

Nicholas Ivie, 30, was among two Border Patrol agents shot on Tuesday in a well-known smuggling corridor near the tiny border town of Naco. The other agent's wounds were not fatal. A third agent in the incident was unharmed.

Mexican officials have said that two men were taken into custody in a military operation near the city of Agua Prieta, a few miles across the border from the shooting. But U.S. authorities have declined to comment on the arrest and details about the incident remained sketchy.

"He really did love the people that he worked with and he was a hero," Ivie's older brother, Chris, told reporters in Sierra Vista, Arizona, where the slain agent lived with his wife and two young daughters.

About three dozen family members attended the news conference, including Nicholas Ivie's widow. He was the youngest of five siblings from Provo, Utah.

Chris Ivie said that once while on patrol his brother came across a pregnant woman near the border, her feet badly cut up and wrapped in rags.

"He carried that woman a mile and a half ... to where she could receive the proper help that she needed," Chris Ivie said, without elaborating on the woman's fate.

Nicholas Ivie became the fourth Border Patrol agent to die in violent circumstances in less than two years in Arizona, heightening concern about border security in a state already at the forefront of the national immigration debate.

Cochise County Sheriff's spokeswoman Carol Capas said on Thursday that her deputies rushed to the scene after they were contacted by a Border Patrol command center.

She said Border Patrol Search, Trauma and Rescue agents sought to apprehend two men but they managed to flee across the border to Mexico. Her office is pursuing a parallel investigation with the FBI.

Attorney General Eric Holder said on Thursday that the investigation is ongoing, but declined to elaborate at a news conference in Washington.

(Additional reporting by Paul Ingram in Tucson; Writing by Dan Whitcomb; Editing by Cynthia Johnston and Will Dunham)