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Flowers, balloons and notes were among the items left at a makeshift memorial to Deputy Darren H. Goforth at the Houston gas station where he was killed Friday night.Credit James Nielsen/Houston Chronicle, via Associated Press

HOUSTON — A 30-year-old Houston man was arrested Saturday in the fatal shooting the night before of a sheriff’s deputy who was filling the gas tank of his patrol car.

At a news conference Saturday afternoon, the Harris County sheriff, Ron Hickman, identified the gunman as Shannon J. Miles and said that he had been arrested on capital murder charges for a “senseless and cowardly act.”

The deputy, Darren H. Goforth, 47, a 10-year veteran of the Harris County Sheriff’s Office, pulled into a Chevron gas station at about 8:30 p.m. on Friday along a busy, tree-lined stretch of suburban Houston about 25 miles from downtown.

As Deputy Goforth pumped the gas, the gunman approached from behind and began firing, continuing to shoot after the officer fell to the ground, the authorities said. Investigators have not found any provocation that might have set off the attack.

“We have not been able to extract any details regarding a motive at this point,” Sheriff Hickman said. “As far as we know, Deputy Goforth had no previous contact with the suspect. It appears at the outset to be completely unprovoked.”

Deputy Goforth “was a target because he wore a uniform,” the sheriff said.

Investigators recovered a handgun that ballistics tests indicated was a match to the weapon used in the shooting, Sheriff Hickman said, adding that the police were not searching for any other suspects.

Even as officials at an earlier news conference emphasized that they had not established a motive, they tied the attack to the wave of protests across the country over police shootings, including the demonstrations after the deaths of Michael Brown in Ferguson, Mo., and Eric Garner on Staten Island.

To some, the death of Deputy Goforth echoed the attack last year on two New York City police officers who were sitting in their patrol car in Brooklyn when they were shot at point-blank range and killed. The gunman, Ismaaiyl Brinsley, who had a history of mental health problems, had traveled to the city from Baltimore, vowing to kill officers, and had alluded to the Brown and Garner cases on social media.

“At any point when the rhetoric ramps up to the point where calculated, coldblooded assassinations of police officers happen, this rhetoric has gotten out of control,” Sheriff Hickman said. “We’ve heard ‘black lives matter.’ All lives matter. Well, cops’ lives matter, too. So why don’t we just drop the qualifier and just say ‘lives matter,’ and take that to the bank.”

The Harris County district attorney, Devon Anderson, who appeared with Sheriff Hickman, said it was time for “the silent majority” to come forward to support law enforcement.

“There are a few bad apples in every profession,” she said. “That does not mean that there should be open warfare declared on law enforcement.”

State Representative Garnet F. Coleman, a Houston lawmaker who is heading a legislative inquiry into the death of Sandra Bland, an African-American woman found hanging in a Waller County jail cell in July, criticized the sheriff’s remarks.

“It strikes me as politicizing a death that, I don’t know that anyone knows what was in the mind of the shooter,” said Mr. Coleman, a Democrat. “I think black lives matter. I think deputy sheriffs’ lives matter. But I think the statement shows a lack of understanding of what is occurring in this country when it comes to the singling out of African-Americans.”

DeRay Mckesson, 30, an activist who has attended and publicized several protests, from Ferguson to North Charleston, S.C., said in a Tweet that it was “sad that some have chosen to politicize this tragedy by falsely attributing the officer’s death to a movement seeking to end violence.”

Mr. Miles lives about a half-mile from the gas station where the shooting occurred. A relative inside the house declined to comment. Around 6:30 p.m. Saturday, a woman drove up and stuck a sign in the lawn with a passage that read, “Father, forgive them.”

Some of Mr. Miles’s relatives stepped outside to look at the sign, and one walked to the corner, said she had no comment, pulled up the sign and carried it inside.

The shooting stunned Harris County, the most populous in Texas, with 4.4 million residents. Sheriff Hickman said he had been in law enforcement for 45 years and could not recall another episode as “coldblooded and cowardly.”

Gov. Greg Abbott, in a statement, said that “heinous and deliberate crimes against law enforcement” would not be tolerated in Texas.

On Friday evening, Deputy Goforth responded to a vehicle accident nearby and then went to the gas station. Investigators were looking into whether the accident and the shooting were connected, but Sheriff Hickman said that did not appear to be the case.

Deputy Goforth was married and had two children, ages 5 and 12. Rick Hartley, the executive director of the 100 Club, a volunteer group that provides assistance to the children of firefighters and law enforcement officers killed in the line of duty, said it would give Deputy Goforth’s family a check for $20,000 to help with immediate needs.

The president of the Harris County Deputies’ Organization, Deputy Robert Goerlitz, said he had known Deputy Goforth since 2008 and described him as a “wonderful family man” who had spoken often of his wife and children.

“He was an extremely hard worker,” said Deputy Goerlitz, who was Deputy Goforth’s patrol instructor at the sheriff’s academy. “I’ve seen some dedicated folks, but he was above and beyond.”

Deputy Goforth had experienced effects of previous injuries while he was in the academy but pushed them aside during his training. “He wouldn’t give up,” Deputy Goerlitz said.

At the gas station on Saturday afternoon, the pump where the deputy was shot, No. 8, was turned into a makeshift memorial. Someone attached a piece of paper to the pump’s computer screen with a message reading, “Gone but never forgotten, R.I.P. Deputy Goforth.”

On the pump and below it, people left bouquets of roses, teddy bears, American flags, balloons, police patches and notes. A small crowd of men, women and children gathered around it throughout the day in a quiet vigil, even as the gas station reopened for business.

Wes Tarpley, 60, who lives nearby, left a cross at the base of the pump that read, “Grace and peace my son.” He said he could not make sense of the killing.

“You can’t make sense of evil,” Mr. Tarpley said. “Evil is evil. There’s no rhyme or reason to it. I don’t know what was going on in that young man’s life. Whatever it was, it was dark.”

Sheriff Hickman and other officials said they had been overwhelmed by the support of residents and other law enforcement agencies. But he said his deputies, while being more cautious as they worked their shifts, were reeling.

“This is the kind of thing that drives you right down to your soul,” he said. “Our job is to carry the badge and gun and protect everybody else, and now we’ve got to fall back, regroup and take care of one of our own.”