Austin Tice, of Houston, Texas, disappeared in August 2012 while covering Syria's civil war.
A video released a month later showed the journalist blindfolded and held by armed men, saying "Oh, Jesus." He has not been heard from since.
"I am here asking for information and for help to find my son and bring him safely home," Debra Tice said at a news conference in Beirut marking more than 1,000 days since his disappearance.
"Someone possibly near this place knows something about my son and his whereabouts," she said. She delivered her statement south of Beirut, near a main stronghold of Lebanon's Hezbollah movement.
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The armed Shiite group has sent thousands of fighters to Syria to battle alongside President Bashar Assad's troops.
"Are the holders of my son ready to meet face-to-face with one individual alone and let him meet with my son? A friend of the family and known by some Shiite leaders in Lebanon and beyond?" she said.
"The Syrian government denies holding Austin, but we think it can help us bring him back safe and sound," Deloire said.
Tice said "we have every reason to believe Austin is alive. As recently as a few weeks ago and a number of times over the past 33 months credible sources have told us Austin is alive."
"We are grateful to his captors for keeping him well and safe. Can my son be allowed these days to communicate with me by phone while I am in Beirut?" Tice asked.
Tice said that for more than two years "we have been urging our government to directly engage with the Syrian government to find our son and secure his release.