SANGIN, Afghanistan—Somewhere in this dusty town, concealed among the cornfields, irrigation canals and mud-walled compounds, is a man the Marines particularly want to kill.

They don't know what he looks like. But they know he is a very good shot with a long rifle, and, every day he remains alive, he is drawing Marine blood.

In the seven days since the men of Lima Company, Third Battalion, Seventh Marine Regiment arrived in town, the Sangin sniper has persecuted them with methodical, well-aimed shots, fired one at a time. His toll so far: two men killed—one American and one British—and one man wounded.

Two Marines have survived hits they say came from a second shooter, believed to be less proficient and careful than the first.

Sangin has for years been a hotbed of insurgent activity in volatile Helmand province, and, in its first days here, Lima Company has pressed through a belt of farmland between the Helmand River and a main road, Route 611. The Marines have been met with hidden explosives and ambushes.

But the sniper has caused the most damage—a deadly reminder that the Taliban insurgency has its share of well-trained fighters capable of frustrating the allied mission.

"He's hitting people—that's very disruptive," said 1st Sgt. John Calhoun, 41 years old, from Konawa, Okla. "But it's not interfering with what we're trying to do here."

The sniper struck first on Aug. 13, the day after Lima Company arrived. A Marine stepped out of his armored vehicle just 100 yards or so from a secure U.S.-British patrol base. He threw away some trash and exchanged a few words with another Marine. The sniper fired a single, lethal shot.

On the same day, a British army engineer—20-year-old Darren Foster from Carlisle, England—was in a guard post in front of the same patrol base. British troops have built a covered, bunkered pathway so the guards aren't exposed to enemy fire as they walk down from the hilltop base. The post is protected by bulletproof glass, except for small gaps through which the guards fire their weapons. The sniper timed his single shot and killed the engineer as he walked past the opening.

"He hit a moving target in a space this big," said Capt. Jim Nolan, Lima Company's commander, holding his hands about nine inches apart.

On Aug. 14, a U.S. tank mechanic took a round in the torso as he carried sandbags across a small bridge. The protective plate in his body armor stopped the round.

"We think it's the same guy," said Gunnery Sgt. Edward Rivera, 39, of Poway, Calif.

Other Marines believe the evidence suggests a second shooter, less accurate and armed with a smaller-caliber weapon.

Then on Sunday, the snipers hit twice. First, Lance Cpl. Derek Simpson took a round to the head.

One of the Marines' tank-like mine-clearing vehicles had slipped off of a dirt bridge, knocking the track off the sprocket wheel. The Marines hitched it to a tow-tank and pulled until the track came completely free, then set to work putting it back in place. Lance Cpl. Simpson, of Third Combat Engineer Battalion, was working on the project and talking to some other Marines when he felt a hard blow to his head.

The sniper's bullet had apparently hit the tank and ricocheted into the front right side of Lance Cpl. Simpson's helmet. It punched into the Kevlar shell, but didn't penetrate all the way.

Lance Cpl. Simpson, who was raised in Gary, Texas, can't recall if he was knocked to the ground or threw himself there to avoid another shot. Another Marine dragged him to cover. He lay on his back as a friend pulled off his helmet to reveal a bloody welt on the right side of his forehead. Two Navy corpsmen, the Marine equivalent of Army medics, decided against stitches.

"I feel blessed," he said. But he also felt guilty for leaving his comrades. "I want to be out there with everyone else," he said. "It's not fair that I'm alive and in here, and they're still out there."

Fifteen minutes after Lance Cpl. Simpson arrived at the patrol base, another Marine went down near the same spot. Again, just one shot.

The other Marines pulled him, too, behind an armored vehicle, where a corpsman treated his wounded leg. The men called frantically for an armored ambulance, but were relieved that the corpsman found the bullet had missed the femoral artery. The wound wasn't life-threatening.

Back at the patrol base, Sgt. Johnny Bailey watched a live video feed of the scene at the bridge and tried to find out which way the Marine had fallen. "That way I'll know the direction of the shot," he said.

The Marines send their own snipers out hunting. The Marine scout-snipers, who go through extensive training, are reluctant to grant that title to the insurgent gunman. They might allow him "marksman," a lesser honorific.

"He's a decent shot—not a great shot," one Marine sniper said as he headed out the patrol base to try to kill the insurgent. He had heard the thump and crack of each of the sniper's shots. He estimates from the sound that the Sangin sniper is less than 600 yards away from his targets. Still, the Sangin sniper appears careful and clever.

During the U.S.-led offensive earlier this year in Marjah, another Helmand province hot spot, one insurgent sniper positioned himself two or three rooms deep inside a building, concealed well enough to hide the flash of his rifle's muzzle. His shots would travel room-to-room through the building, exit through a small hole in the exterior wall and hit Marines on a rooftop outpost. It took Marine snipers days to locate and kill him.

Write to Michael M. Phillips at michael.phillips@wsj.com