USAF Academy via AP

The U.S. Air Force has identified Capt. Lucas Gruenther, seen here in 2003, as the pilot of an F-16 fighter jet that went missing Monday on a training mission over the Adriatic Sea.

The body of a U.S. Air Force pilot whose F-16 fighter jet went missing Monday after it took off for a training exercise from Aviano Air Base, Italy, has been found in the Adriatic Sea.

According to a statement released by the family, the body of Capt. Lucas Gruenther, 32, was found Thursday afternoon.

"A compassionate husband, a loving son, and a devoted brother; Luc leaves behind a family who loves him dearly and a legacy of achievement," the statement reads. "We will never fully recover from our loss, but take heart in the knowledge that during his all-too-short time in this world, he made a significant difference in the lives of all whom he met."

The Air Force also issued a statement, offering condolences to the family.

"Captain Gruenther was an outstanding officer who epitomized what it means to be an Airman," said Brig. Gen. Scott J. Zobrist, 31st FW commander. "He was not only a first-rate pilot; he was an exceptional leader whose presence will be sorely missed."

The statement said Gruenther, an Air Force Academy graduate, had flown numerous combat sorties during a six month deployment to Afghanistan in 2011, and that a board of officers will investigate the incident.

Earlier in the week, fragments of carbon steel and other debris were found floating in the northern Adriatic. At the time, the Air Force said it believed the debris belonged to the wreckage of the missing aircraft and continued its search-and-rescue operation.

The family kept its hopes up, and in a blog post published on the base's website, his wife, Cassy, wrote: "If anyone could survive something like this, it would be Luc."

Officials then confirmed that Gruenther's drogue parachute and his helmet were among the debris found in the water. Cassy wrote that they remained optimistic, as they were told the helmet was found in good shape.

"That's why I know he's coming home," Cassy wrote in the blog post. "If he has his mind set on something, he will find a way to make it happen. He'll find a way; whatever he has to do."

NBC Bay Area said Gruenther was from Twaine Harte, Calif. He married his high school sweetheart, who is expecting the couple’s first child, Serene, in a few weeks.

The Gruenther family thanked "the many people who volunteered their time and resources to help bring Luc home." The search operation included aircraft and ships from the United States and Italy.

NBC New staff writer Kari Huus contributed to this report.

Alessandro Garofalo / Reuters, file

A U.S. Air Force F-16 fighter jet like the one shown flying over Aviano Air Base, Italy, is presumed to have crashed in the Adriatic Sea while on a training exercise. Aviano controllers lost contact with the plane about 8 p.m. local time Monday.

U.S. and Italian authorities searched the Adriatic Sea on Tuesday after a U.S. Air Force fighter jet was lost and presumed to have crashed.

Divers focused on waters where a fishing boat had found fragments believed to belong to the F-16, a Coast Guard official told Reuters.

Fragments of carbon steel and other debris were found floating in the northern Adriatic overnight, Rear Admiral Francesco Saverio Ferrara told Reuters. The U.S. Air Force said in a statement it believed the debris belonged to the wreckage of the missing aircraft, Reuters reported.

"We hope to find out more during the day so we can have a more complete picture of what happened," Ferrara said, according to Reuters.

Controllers lost contact with the F-16 at about 8 p.m. local time (2 p.m. ET) Monday, after it took off for a training exercise from Aviano Air Base, Italy, the Aviano-based 31st Fighter Wing said in a statement.

Italian aircraft and ships were dispatched to the missing jet's last known location, and U.S. and Italian aircraft were flying over the area Tuesday, the Air Force said.

The Italian national news agency ANSA reported that a fuel slick was seen off the coast near the town of Cervia and that a fishing boat had found fragments that could have belonged to a military jet.

Weather was bad at the time the plane vanished, with sleet falling and visibility poor, the Associated Press quoted an Italian coast guard commander as saying. 

The Italian news agency LaPresse reported that the pilot sent an alarm signal to Aviano before contact was lost and that three other planes on the training mission had made it back to the base safely.  

No information was released about the pilot, who was the plane's sole occupant.

Search-and-rescue operations are still being conducted by sea and air, Reuters reported.

"Wing leadership remains hopeful that we will safely rescue our pilot," an Air Force statement said, according to Reuters.

The Associated Press, Reuters, ANSA and LaPresse contributed to this report