"However, in the meantime, the said company has taken all the 29 employees into their custody and is holding them captive in a room at Allsafaniya Kouqt, Bodar, city Kanji, Saudi Arabia, denying them food/water or medicines and other basic amenities for the last 12 days," Telangana NRI Affairs Minister KT Rama Rao said in a letter to Ms Swaraj.
The 29 employees sought leave to visit their hometowns, but the company demanded $50,000 each to relieve them. It also refused to provide travel expenses, Mr Rao said in the letter.
The employees approached a court for justice and got a decision in their favour, but they were being "held captive" by the employer, he said.
"Having full faith in the alacrity of your response, for which your Hon'ble authority is known, I reiterate my request, for immediate intervention, on humanitarian grounds to save the lives of 29 migrants from the state of Telangana," Mr Rao added.