"All those involved in the incident in the Curonian Lagoon are already in Lithuania. The handover procedure has been completed," Vytaute Smaizyte-Kuliesiene, spokeswoman for the foreign minister, told BNS on Sunday evening.
The three men were handed over to Lithuanian officials at the Panemune border post.
Markauskas, a former agriculture minister, posted on Facebook on Sunday evening that he regretted the incident, saying that he crossed the state border accidentally while fishing.
"While fishing in the Curonian Lagoon today, I accidentally crossed the Russian state border. I was detained and fined. I regret this incident," the mayor wrote.
"It wasn't a pleasant incident, but I'm on my way home now," he added. "I'd also like to thank our country's consular officials for their promptness and assistance."
The 15min news website reported earlier on Sunday that the other two Lithuanians detained by Russian officers were businessmen Darius Zilinskas and Romualdas Sukys.
Giedrius Misutis, the spokesman for Lithuania's State Border Guard Service, told BNS that a boat crossed into the Russian side of the Curonian Lagoon at about 2 p.m. and was detained by Russian officers, adding that the border violation was most likely unintentional.
Such border crossing incidents occur on both sides of the border, especially in the warm season, he noted.