He said women also seek genetic tests for peace of mind and to prepare themselves and their families if a problem is found. In some cases, procedures can be performed in utero to improve the fetuses' health.
Santorum says President Barack Obama's Affordable Care Act will require insurance companies to cover prenatal tests such as amniocentesis, in which a needle draws out amniotic fluid and cells from the sac surrounding a fetus to test for defects, including cystic fibrosis, spina bifida and Down syndrome.
In a speech to the Christian Alliance in Ohio on Saturday, Santorum said the law was intended to increase abortions and save money "because we cull the ranks of the disabled in our society."
And on the CBS News program "Face the Nation" Sunday, Santorum added: "Amniocentesis does in fact result more often than not in this country in abortion. That is a fact."
In Utah, the numbers tell a different story.
Among all pregnancies with a birth defect, 4.2 percent resulted in termination between 2000 and 2009, according to the Utah Birth Defect Network. During the same time period, 9.6 percent of fetuses with Down syndrome were terminated.
A 1999 study showed that nationally, 90 percent of women terminate their pregnancies after a prenatal diagnosis of Down syndrome.
While Santorum said women have a right to do the tests, "to have the government force people to provide it free, just to me is a bit loaded."
In Utah, Medicaid currently covers some prenatal tests, including amniocentesis, according to the state health department.
The Obama campaign says prenatal testing is "essential to promote the health of both the mother and baby and to ensure safe deliveries."
After two of her children died from suspected mitochondrial disease, Lehi mother Marie Nuccitelli wished there was a prenatal test to detect the disorder to "get the shock out of the way [so] you can focus more on the needs your child has."
Instead, when she found out she was pregnant with her now 3-year-old, she met with a genetic counselor to understand the risks. She learned there was a 25 percent chance her daughter would have the disorder, which can damage the cells of the brain, heart, liver, skeletal muscles, kidneys and the endocrine and respiratory systems. It can be fatal.
"I'm not a person that really looks at termination as an option," said Nuccitelli, a Republican. "It was a way for me to kind of prepare after going through what we have been through. I didn't want to go through it again. I also felt like if I knew it was coming it would help me to deal with it rather than be surprised."
Her daughter Sarai does appear to have the disorder.
Nuccitelli is hesitant to support insurance mandates hoping insurance companies would voluntarily cover it. "It's a very personal decision for families to make."
Erin Hayes, of Taylorsville, didn't terminate her pregnancies after prenatal testing showed two of her daughters had fatal chromosomal abnormalities, including Trisomy 16, which meant they had three copies of the particular chromosome instead of two.
Hayes said a neonatologist, who is no longer working in Utah, had told her to abort when she found out about her first daughter, Charlotte. She considered but rejected the idea and believes fewer doctors would push such views on patients today and prepared herself that the girl would be stillborn or die within hours.
Instead, the girl, who loved dogs and liked to laugh, lived until she was almost 4. "She had the best little personality. It was so fun. Our lives are so much richer for having had her."
Hayes had another amnio with a later pregnancy not because she planned to abort, but to prepare.
After the bad news, she tried to enjoy her pregnancy knowing it "might be the only time I have with my baby… and try and bond with her and not focus on what's to come."
Lily died after three months.
Hayes, who says she will likely support Obama in the election, says insurance should cover the tests. "Some people are going to get an abortion no matter what. Right now, that's their right."
Prenatal test results can guide care for women who are carrying children with birth defects, even fatal ones, agrees Intermountain Medical Center physician Nancy Rose, director of Reproductive Genetics for Intermountain Healthcare.
Nancy Rose, director of Reproductive Genetics for Intermountain Health Care.
"If a woman finds she's having a baby that's going to have an outcome not compatible with life, we can work it out so the baby doesn't have to be torn away from the mom or [undergo] aggressive resuscitation."
She said insurance companies should cover the tests "so people don't make decisions based on money but based on what's right for their family needs."
The Associated Press contributed to this story.