Martin took the baby, wrapped it in an empty sand bag and made a dash to the pick up zone.
"I didn't think twice, but it did cross my mind if we got hit by enemy fire, what would I do with a baby in my arm," he said.
"But luckily that didn't happen and we got the little girl to safety."
After informing his commanders, the military helicopter was diverted to the Quang Tri Catholic Hospital where the baby was left.
"The nuns asked me for a name, and my platoon mates suggested to name her after me," Martin said.
"Roberta, after Robert and Sunday as her last name because she was found on a Sunday."
Now 71 and living in Idaho, Martin is the commander of the United States Veterans of Foreign Wars (VFW) Post 889 in Coeur d'Alene.
After a friend had reconnected with the daughter of a Vietnamese soldier he had shot, Martin said he desperately wanted to also find Roberta Sunday.
He'd thought about her a lot over the last 47 years, and decided last year to re-connect with her.
"I saved this little girl, and God it'd be nice to know the results of my action," Martin said.
"It's nice to have closure because it's been kind of a mystery to me about what happened after we left her at the hospital."
Martin believes the woman, who would be 47 now, has been brought to New Zealand by Save the Children.
New Zealand sent nurses and other support workers to Vietnam from 1968 through 1974 to bring orphans from Vietnam to New Zealand.
If she is found, Martin said he would make a trip to New Zealand to see her — but wouldn't really know what to say to her.
"I wonder what she would say to me," he said.
"I've also not given much thought about what I'd say, maybe just 'how's life been treating you?'"
The only lead he has had was through a VFW auxiliary president who came across an article about a blind Asian woman, who appeared to be in her 40s, and was hired by a medical company in New Zealand.
However, efforts to find the article again proved futile.
The VFW has approached New Zealand's Ministry of Foreign Affairs to help with Martin's search.
Martin said rescuing Roberta Sunday was the only "positive memory" he had of the "terrible war".
"Being able to give that girl a chance to live a full life is the only good thing that happened to me in Vietnam," he said.
Save the Children New Zealand has been approached for comments.