"For the most part, they all came on legitimate student visas. It was actually when they were in country that some of them sought to extend their stay in the United States is my understanding," Mark Toner, State Department Deputy Spokesman, said.
These students numbering 306 were caught in a sting operation conducted by Department of Homeland Security and Immigration and Customs Enforcement.
As many as 21 brokers and middle men including 11 people of Indian-origin were arrested last week as a result of the sting operation.
"These individuals who came here on a student visa did come either to work or to study legitimately. They did qualify for student visas. They met the qualifications. They were issued student visas," Toner said.
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"It was only after living here, attending university or whatever, that they then decided to again allegedly seek out the assistance of this criminal organisation to extend their stay in the United States. That's an important clarification," he said.
"They did come here legitimately, on legitimate visas. It's not about a visa issue. It's about once they were here in the United States, they then sought through a criminal organisation to extend their stay," Toner said.
Indian students trapped in the sting operation came to study at American universities as qualified students, he said.
"Once they got here, they were here to a time and they sought to extend their stay here in the United States and that's when they sought to stay here illegally or they sought to - again, this is all allegedly right now," he added.