It was around mile 10 of his marathon in Dubai, but in truth, it was closer to mile 141 for the former GW cross-country runner. Five days earlier, Mr. Cartica and 14 other runners began the World Marathon Challenge, a brutal endurance race through seven marathons on all seven continents in just seven days.

The competitors started the endeavor in Union Glacier, Antarctica, a shining expanse of snow and glaciers that was minus-12 degrees Fahrenheit, despite the 24 hours of sunlight, when the race officially got underway on Jan. 23. After completing their first 26.2 miles of the week, the runners boarded a Russian cargo jet and took off for their next marathon location: Punta Arenas, Chile.

From there it was on to Miami; then Madrid; Marrakech, Morocco; Dubai, United Arab Emirates; and Sydney, Australia, for a marathon in each city.

The Moroccan leg of the race was one of the toughest: When the marathoners stepped across the start line in Marrakech, they did so just a few hours after completing the marathon in Madrid.

"Running the Moroccan leg on such a quick turnaround meant that I had run two full marathons in a 15-hour period and over 100 miles in just a few days," says Mr. Cartica, a captain in the U.S. Marine Corps. "When I hit mile 10 of the next leg in Dubai, the fatigue and depleted nutrition started to take their toll, and that's when the pain started."

As he struggled to keep his pace, his thoughts focused on the reason he was undertaking this grueling journey: to honor the Navy sailor and four U.S. Marines who were killed in Chattanooga, Tenn., on July 16, 2015.

"I knew, without question, that those five individuals would not have contemplated giving up or throwing in the towel, and that was really the mindset I had for the rest of that day," Mr. Cartica says. "So I kept fighting and got through those last 16 miles, but it wasn't pretty."

Less than 24 hours later, he crossed the final finish line in Sydney as the winner of the 2016 World Marathon Challenge. In all, Mr. Cartica finished first or tied for first in all but two of the race's seven stages (when he placed second), setting the world record for the fastest average marathon time for seven marathons on seven continents in seven days.

Mr. Cartica says he hasn't thought much about the record, but feels that maybe 15 or 20 years down the line it'll be an interesting asterisk next to his name. For now, he's hoping people will focus less on how he ran and more about why.

"Getting out the message of why I decided to run this race is the most important thing for me," he says. "The individual, Daniel Cartica, is just a normal guy who set out on this endeavor to honor five servicemen—they're the ones we should be honoring.