In their first sit-down interview, Michael and Susan Pretti avoided recriminations and recalled the son that Michael called “an exceptionally kind, caring man.”

Alex Pretti’s parents keep a box crammed with 200 letters and cards that have poured into their suburban Denver home since their 37-year-old son was shot and killed by immigration agents last month in Minneapolis.

Some are from health-care workers and veterans praising Mr. Pretti’s work as an intensive-care nurse at the Department of Veterans Affairs. Others are from strangers who hail Mr. Pretti as a hero for his final actions, when he tried to help a woman shoved to the ground by a Customs and Border Protection agent, only to be tackled and shot multiple times.

“There’s probably 10 more in the mailbox today,” Mr. Pretti’s father, Michael, said on Tuesday in their first lengthy interview as he and his wife, Susan, held hands and talked about memories of their son, and the nightmare of anger, grief and unanswered questions they have faced since his killing on Jan. 24.

“He’s my first born,” Susan Pretti said. “He’s the one that made me a mother. There was no reason he should have died that day.”

“No,” her husband said.

To the Prettis, that box of letters helps tell the true story of their son, whom they called a curious, big-hearted man dedicated to his family, his nursing patients and his community in Minneapolis.

They said they had not talked politics often with their son, but they knew he was upset about the immigration crackdown that brought about 3,000 federal agents to Minnesota this winter, and knew he had joined thousands of other people in protesting the raids and arrests.

They said he had cherished his community in Minneapolis and had been aghast to see what was happening there.

“He said, ‘Mom, they’re kidnapping kids,’” Mr. Pretti said, recalling a conversation. “‘Why would anybody do that? Why would people treat each other like that? That just doesn’t make any sense. There’s no reason to.’”

Trump administration officials have called their son a domestic terrorist who wanted to “massacre” law enforcement, and blamed him for inserting himself into the tense, sometimes violent immigration protests in Minneapolis while he was carrying a handgun with a valid permit.

Alex Pretti’s parents denounced the administration’s claims in the hours after his death as “sickening lies.” Videos from the scene show that Alex Pretti never drew his gun and was on his knees and had been disarmed by a federal agent a moment before he was shot.

Those videos play on painful repeat in the Prettis’ memories now, they said. Mr. Pretti added that he had to mute the television and shield his eyes if it popped up on the news.

But they said the videos proved their son did not deserve to be killed on a snowy Minneapolis street that morning.

“It’s so clear as to what happened,” Mr. Pretti said.

A family smiles for the camera in front of a staircase.
The Pretti family, from left to right, Michael, Micayla, Alex and Susan.Credit…via the Pretti Family

The parents’ lawyer, Steven Schleicher, who served as a special prosecutor in the murder trial of the Minneapolis police officer who killed George Floyd, said Tuesday that the Prettis were seeking “facts and accountability” and wanted to know the full truth about the federal agents who shot their son and exactly what happened on that street that morning.

The Prettis’ television stayed off on Tuesday as top immigration officials in Washington were testifying to Congress about the administration’s deportation campaign. The officials refused to answer questions about the killings of Mr. Pretti or Renee Good.

The Prettis said they had tried to keep their focus on their son’s life, and not on the uproar touched off by his death.

“The truth is, he was an exceptionally kind, caring man,” Michael Pretti said.

The couple described themselves as a “good Midwestern family” who raised Alex and his younger sister, Micayla, in a tight-knit neighborhood in Green Bay, Wis.

They ate dinner together nearly every night and made their house a destination for play dates and sleepovers. They said they had attended all of their children’s basketball games and track meets and had served as a parental taxi service for practices and trips to the mall and doughnut shops.

From an early age, they said, Alex was curious about how the world worked and what lay beneath the surface.

When Alex was 5 or 6, Ms. Pretti said, she decorated his room with a fish-themed wallpaper border, and he ripped away one section. He told his mother he had just wanted to see what was behind it, she said.

He devoured books about space and science in his room, decorated with a poster of the solar system, and immersed himself in music and theater, playing the guitar and the piano and singing for years with a local boys’ choir.

“He always wanted to know more,” Mr. Pretti said.

As he grew up, his parents said, he tried to fathom why people treated one another cruelly. He had a wide circle of friends and sometimes came home from his Catholic elementary school upset that another student had been bullied.

“There was always an underlying seriousness to him,” Ms. Pretti said.

After graduating from Preble High School in 2006, he attended the University of Minnesota and quickly made Minnesota his home.

He found work as a research assistant and eventually became a nurse at the Veterans Affairs hospital in Minneapolis. He worked overnight at first and would often call his parents after an exhausting shift.

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A man in glasses looks at his dog in his car.
“We really ramped up, ‘Be careful,’” Michael Pretti said after Alex told him of the first incident with federal agents.Credit…via the Pretti Family

His parents said that Alex had told them about an earlier confrontation with federal agents that occurred on Jan. 13. Video of that incident shows him spitting toward an agent and kicking the taillight of a vehicle before agents tackle him and briefly detain him. He appears to be carrying a handgun at his back during that incident.

The incident came up during a regular check-in with his parents, and Alex told them he had been hurt but was fine. He did not go into detail, they said, but they told him to be careful — a caution they always gave both children at the end of nearly every phone conversation.

“We really ramped up, ‘Be careful,’” Michael Pretti said, and Alex responded, “I will.”

Some critics have pointed to that earlier confrontation as evidence that Alex Pretti was aggressive. But the parents’ lawyer, Mr. Schleicher, has responded, “nothing that happened a full week before could possibly have justified Alex’s killing.”

They last spoke to Alex a day before his death. His garage door had broken in the subzero cold, and Michael Pretti said he had helped arranged a repair from afar. He said Alex had called on Friday to report that the door was fixed and that he had tipped the repairman $100.

When they saw the video of their son’s death, the Prettis said they saw their son’s character showing through.

“His last act on this earth, his last thought, was to help this woman,” his father said.

“It’s who he was, every day,” his mother said. “He’s the same Alex he always was.”

Memories of Alex have been flickering through his parents’ minds almost nonstop, they said, as they try to figure out when they can return to work and begin to plan for a private memorial service for him later this spring.

They have been thinking about how, as a boy, he would help his younger sister walk up and down the stairs. How he would call up his parents to describe his latest tweaks to his mountain bike. And as a child, how he would ask his parents, “If you could push a button” to make anything happen, what would it be?

“If we could push a button,” Mr. Pretti said, “we’d have Alex back with us.”