Albert Calibet, 59, disappeared on the island of Amorgos on Tuesday while following a route toward the village of Katapola, the Amorgos municipality said on its official social media.
The L.A. County Sheriff's Department on Thursday confirmed that a missing persons report has been filed and the department's Homicide Bureau is handling the case locally, in addition to efforts abroad.
According to the department, Calibet worked for the department's Transit Service Bureau since April 1998. After his retirement in 2018, he continued to serve as a part-time employee.
"A 120-day contract employee is a retired Department member in good standing who has elected to work hourly for a maximum of 120 days per calendar year to assist with staffing shortages," the department said.
Authorities said search efforts have extended internationally as Greek authorities deploy search and rescue teams. Anyone with information about Calibet's disappearance is urged to call the sheriff's Homicide Bureau at (323) 890-5500.
"Our thoughts and prayers are with Deputy Calibet's family and friends and our hope is that we can bring him home safely," Sheriff Robert Luna said in a statement "We are actively collaborating with multiple agencies abroad to provide assistance in the search for Deputy Calibet and will use every resource we have available to bring him back to those who love him."
Popi Despotidi, Amorgos' deputy mayor of tourism, told CNN on Thursday that Calibet has been coming "to Amorgos almost every year" for about a decade.
Calibet's friend, Robin Winston, says he was on a well-traveled path and was supposed to meet a friend at the end of the path.
According to people in Greece with knowledge of the case, a group of walkers met up at 7 a.m. Tuesday. There's confirmation that Calibet was seen at 11 a.m. at a small refreshment stand to get water.
A friend was waiting at the end of the hike, but Calibet never showed up. That friend tried calling Calibet on the phone, but he didn't answer, so his friend reported him missing with local authorities.
"Now we're able to narrow the search area a little bit because we can go an hour further down the path," Winston said. "That's a bit of optimistic news we got this morning but other than that, we're still... It's a four, five-hour trail, they should've been able to see him on the trail by now."
Calibet's brother, who also lives in Southern California, was on the way to Greece Thursday morning to help out in the search.
"They don't have the resources that we have here, so we've got friends in France who are on their way there to do their own ground searches. We've got people on that island who've met Albert and love Albert, and they're searching too, but there's not a lot of people," Winston said.
Authorities on the island had to call off the search for the evening, because they did not have flashlights. Local authorities are hoping to obtain infrared drones in the area to conduct a night search.
Other tourist missing in Greece
Meanwhile, on the island of Samos, a 74-year-old Dutch tourist has been missing since Sunday, with a large search and rescue operation underway, authorities said. The man had gone hiking in the Marathokampou area of the island, the Hellenic Rescue Team of Samos said in a post on Facebook on Wednesday. Local residents are helping with the search, it added.
Konstantia Dimoglidou, a spokesperson for the Greek police, told CNN on Thursday that "police, fire brigade and volunteers are involved in the search, including by air," for both men. "Unfortunately, so far we have no news about either of them," she added.
The news of the disappearances comes just days after the body of British TV personality Michael Mosley was discovered after he vanished while walking in sizzling temperatures on the Greek island of Symi.
Mosley, a television doctor who popularized a type of intermittent fasting known as the 5:2 diet, was reported missing by his wife after he failed to return from a walk on the island. It took several days to find his body.
Greece is currently enduring a blistering heatwave that looks set to peak on Thursday, according to the Hellenic National Meteorological Service, which has released an orange warning for heat - the second-most serious designation.
Authorities closed down the Acropolis in Athens during the afternoon on Thursday for a second day as the country swelters under unseasonably high temperatures.
All other archaeological sites in the Greek capital were also shut during the same hours. People who had booked visits for that period could use their tickets later in the day until the sites close at 8 p.m., the ministry said.
Temperatures exceeded 104 Fahrenheit on Thursday in much of central and southern Greece, including greater Athens, the Cyclades and Crete.
The Associated Press and CNN Wire contributed to this report.