More than 5,000 pregnant Russian women have entered Argentina in recent months, including 33 on a single flight on Thursday, officials say.
The latest arrivals were all in the final weeks of pregnancy, according to the national migration agency.
The number of arrivals has increased recently, which local media suggests is a result of the war in Ukraine.
Of the 33 women who arrived in the Argentinian capital on one flight on Thursday, three were detained because of "problems with their documentation", joining three more who arrived the previous day, migration agency head Florencia Carignano told La Nacion
The Russian women had initially claimed they were visiting Argentina as tourists, she said.
"In these cases it was detected that they did not come here to engage in tourism activities. They acknowledged it themselves."
She said the Russian women wanted their children to have Argentinian citizenship because it gave more freedom than a Russian passport.
Having an Argentine child also speeds up the citizenship process for parents. As it stands, Russians can travel visa-free to only 87 countries.
A lawyer for the three women who were detained on Thursday said that they are being "falsely imprisoned", as they are being held on suspicion of being "false tourists". This is a term "which does not exist in our legislation," Christian Rubilar said.
"These women who didn't commit a crime, who didn't break any migratory law, are being illegally deprived of their freedom," he added.
The women have since been released.
La Nacion attributed the dramatic uptick in arrivals of Russian citizens to the war in Ukraine, saying that "besides fleeing war and their country's health service, [Russian women] are attracted by their [right of] visa-free entry to Argentina, as well as by the high-quality medicine and variety of hospitals".
"Birth tourism" by Russian citizens to Argentina appears to be a lucrative and well-established practice.
A Russian-language website seen by the BBC offers various packages for expecting mothers who wish to give birth in Argentina. The website advertises services such as personalised birth plans, airport pick-ups, Spanish lessons and discounts on the cost of stays in "the best hospitals in the Argentinian capital".
The packages range from "economy class", starting at $5,000 (£4,144), to "first class", starting at $15,000 (£12,433).
The website says its founder has been facilitating birth tourism and offering migration support since 2015, and the company says it is "100% Argentinian".
On Saturday, La Nacion reported that Argentinian police has been carrying out raids as part of an investigation into a "million-dollar business and illicit network" that allegedly provided pregnant Russian women and their partners with fake documents issued in record time to allow them to settle in Argentina.
Police said the gang charged up to $35,000 (£29,011) for the service.
No arrests were made, but police were said to have seized laptops and tablets as well as immigration papers and significant quantities of cash.