A senior official from Crime Investigation Department (CID) in the eastern state of West Bengal said the arrests began on Monday after police raided a private nursing home and found two babies hidden in cardboard boxes in a locked medical storeroom.
Those arrested included the owner, midwives and other staff at the nursing home in Baduria, 80 km from Kolkata.
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Police have also arrested court clerks suspected of making fake documentation for the children and the head of a charity which ran the adoption centre.
"The inquiry is underway and more information will be revealed only after some more progress is made," Bharat Lal Meena, Deputy Inspector General for the CID in West Bengal, told the Thomson Reuters Foundation.
Staff at the nursing home and the charity were not immediately available for comment.
Police said initial investigations indicated that unmarried girls and women who visited the clinic for an abortion were persuaded by staff to give birth and sell their babies.
The police did not give a price, but local news reports said the mothers were given 300,000 rupees ($4,380) for a boy and 100,000 rupees ($1,460) for a girl.
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Babies were also stolen from women who delivered at the clinic, but who were told by staff that their children were stillborn. Some were even shown the bodies of stillborn babies preserved by the clinic to dupe parents, police said.
The babies, mostly newborns, were then smuggled in cartons used to store biscuits, and taken by road to an adoption centre 25 km (15 miles) away in Machlandapur, where they were sold on to childless couples.
"It was a well organized syndicate, incorporating all kinds of helping hands needed for the smuggling network," said another CID official, who did not wish to be identified because he is not authorised to speak to reporters.
The CID officer said more arrests were likely in the coming days.
Reports of human trafficking in India increased by 25 percent in 2015 compared to the previous year, with more than 40 percent of cases involving children being bought, sold and exploited as modern day slaves, government crime data shows.
The National Crime Records Bureau (NCRB) said there were 6,877 cases related to human trafficking last year against 5,466 in 2014, with the highest number of cases reported in the northeast state of Assam, followed by West Bengal state.
South Asia, with India at its centre, is one of the fastest-growing regions for human trafficking in the world.
Gangs sell thousands of victims into bonded labour every year or hire them out to exploitative bosses. Many women and girls are sold into brothels.
India, alone is home to 40 percent of the world's estimated 45.8 million slaves, according to a 2016 global slavery index published by the Australia-based Walk Free Foundation.
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