SAN DIEGO -- A Honduran woman affiliated with a caravan of Central American migrants gave birth on U.S. soil shortly after entering the country illegally amid growing frustration about a bottleneck to claim asylum at official border crossings.

Border Patrol agents arrested the woman Nov. 26 after she entered the country illegally near Imperial Beach, California, across the border from Tijuana, Mexico, Customs and Border Protection said Wednesday. She was arrested with her 20-year-old husband and 2-year-old son.

The woman, who was eight months pregnant, was taken to a hospital after complaining about abdominal pain the day after her arrest, Customs and Border Protection said. The family was released from custody on Sunday, pending the outcomes of their immigration cases.

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Univision reported that the family is seeking asylum and hoped to join family in Columbus, Ohio, while their cases are pending. Maryury Serrano Hernandez, 19, told the network giving birth in the U.S. was a "big reward" for the family's grueling journey.

Scores of pregnant women have traveled with the caravan through Mexico before reaching the U.S. border. In Pijijiapan in the southern state of Chiapas, Dr. Jesus Miravete, who volunteered his services in the town's plaza, said he treated a few dozen pregnant women, including 16 for dehydration after being on the road for weeks.

President Donald Trump said in October that he could end birthright citizenship with a swipe of his pen. Most scholars on the left and right share the view that it would take a constitutional amendment to deny automatic citizenship to children born in the U.S. to parents who are in the country illegally.

U.S. inspectors at the main border crossing in San Diego are processing up to about 100 asylum claims day, leaving thousands of migrants waiting in Tijuana. Some are crossing illegally and avoiding the wait.

Of the more than 6,100 migrants staying in a temporary shelter run by the city of Tijuana last week, 3,936 were men, 1,147 were women, and 1,068 were children.

Those who present their asylum cases await tough odds. The American asylum process requires people to prove they've fled persecution at home, and more than 75 percent of asylum cases from Central America were denied from 2012 to 2017, CBS News' Adriana Diaz has reported.