"I'm not going on record as saying anything," Lunden says when asked by Barbara Walters (search) in an interview airing tonight (10 p.m.) on 20/20.
Lunden does, however, say that Konigsberg's sperm was used to fertilize the eggs.
"We've really taken the position that we want to not be public about how we go about creating our children," she says.
Lunden says that the surrogate mother, Deborah Bolig, has no biological connection to the twins, and that none of the eggs came from anyone in Lunden's family — including her three grown daughters (Jamie, Lindsay and Sarah) from her marriage to Michael Krauss.
Lunden, 52, announced last March that she and Konigsberg, 42, were going the surrogacy route in having children.
Bolig gave birth last month to twins Kate and Max.
Lunden also reacts to criticism from some corners that she's too old to have children — that she will be 65 when the twins enter their teen years.
"Is it fair for a 16-year-old girl to have a baby and not really take great care of it because she's a little girl herself. . . Families are made in many, many different ways today," she says.
"I particularly am a person who is really very health-conscious and fit."
And, Lunden says, she might have more kids.
"Possibly. We have more embryos," she tells Walters. "We might do that [surrogacy]."