"It is now OK to argue even in our nation's capital or in the state capitals or in the universities that fathers do matter and marriage is good," Quayle told a National Press Club luncheon audience Thursday.
Quayle, 55, vice president under George Bush from 1989-1993, said also the global fight against terrorism is a fight for families.
"We are fighting for the preservation of our families and we are fighting for the preservation of our freedoms," Quayle said. He said a nation "is only as strong as its families."
Quayle's 2,700-word speech at the Commonwealth Club of California in San Francisco on May 19, 1992, sparked controversy with its one-sentence reference to "Murphy Brown," a fictional television journalist played by Candace Bergen.
Quayle said he was trying to highlight the responsibilities of fathers and their need to be involved in the lives of their children. The passage that mentioned Brown said:
"Bearing babies irresponsibly is, simply wrong. Failing to support children one has fathered is wrong. We must be unequivocal about this. It doesn't help matters when prime time TV has Murphy Brown -- a character who supposedly epitomizes today's intelligent, highly paid, professional woman -- mocking the importance of fathers by bearing a child alone, and calling it just another 'lifestyle choice.'"
Quayle said in the show, the father was completely uninvolved with Brown's child. By contrast, he said, a current program -- "Friends" -- has a female character who is single and pregnant, but the father apparently planning to be actively involved in the child's life.
"So we have come halfway," Quayle said. He also said in real life, the woman playing the "Friends" character -- Jennifer Anniston -- is happily married to Brad Pitt.
Quayle said 90 percent of the sexual situations shown on television involve sex outside marriage, but the actors and actresses often have solid, stable family lives at home.
Quayle was asked his opinion of Ozzy Osbourne's family reality show -- "The Osbournes" -- on MTV. President Bush and Osbourne traded quips at the White House Correspondents Association dinner Saturday night.
Quayle said he's watched the show once. He said the Osbourne parents give their children the positive messages that they love each other and that they shouldn't abuse drugs or alcohol.
"Underneath, I think there are some very good lessons being transmitted," Quayle said. "I found it rather entertaining."
In speaking about values and responsibility, the former vice president said there is one proven formula for staying out of poverty: Finish high school, wait until marriage to have children, and don't get married until at least age 20.
"If you follow those three things, you have an 8 percent chance of living in poverty," he said. Quayle said those who don't finish high school, have children and marry before 20, have an 80 percent chance of living in poverty.
Quayle called on parents to get involved in the lives of their children by going to parent-teacher conferences, getting to know their friends, and introducing children to a spiritual life and share it with them.
"Remember, it's not necessarily the economy, it's our souls," Quayle said. "But we do need help from the outside. We can't do it just ourselves. We need help from the media, from Hollywood, from academia, from others that have influence on our culture. In the final analysis, it's all of us working together to get this job done."