"We love you, Jaycee, and we're waiting for your call," the man, Ken Slayton, said. "We would like to meet in a private setting very very soon."
Dugard is the Northern California woman, now 29, who was allegedly held captive by Phillip Garrido in a home near Antioch for the past 18 years. Dugard was kidnapped from South Lake Tahoe in 1991. Two UC Berkeley police officers and a parole agent helped crack the case and free Dugard and her two children on August 27. Dugard has since been reunited with her mother.
Slayton is being represented by celebrity attorney Gloria Allred, known for her publicity-seeking ways. He is a 63-year-old Los Angeles resident with four grown children.
Slayton cried though much of the news conference. He said he had a brief relationship with Jaycee's mother Susan back in 1979, but had not been in Jaycee's life since then. He says he wants to change all that.
He said he and his wife and their children are interested in getting to know Jaycee. He said he thinks he can be a positive male role model in her life.
Slayton claims he doesn't want anything from Jaycee and says he is willing to prove his paternity.
Slayton had not previously contacted the Dugard family, a family spokeswoman told the Los Angeles Times.
"This all comes as a big surprise," Spokeswoman Erika Schulta told the Times.
Dugard's alleged kidnappers, Phillip and Nancy Garrido, have each been charged with kidnapping, raping and falsely imprisoning Dugard in their backyard.
Both have pleaded not guilty.