The more than 25-year-old airline temporarily suspended operations on April 17 as it ran out of cash after lenders declined to extend emergency funds.
"In the absence of any emergency funding from the lenders or any other source of funds forthcoming in the near future, we find ourselves facing a situation where we are not able to fund the premium of our Group Mediclaim Policy. The policy lapses on the midnight of April 30.
"These circumstances are not of our doing and much as we would wish to do things differently, we are left with little choice," he said in a communication.
The full service carrier has more than 20,000 employees, including pilots and engineers.
Noting that the group mediclaim policy would cease from May 1, Taneja urged employees to take a medical insurance cover of their choice.
The domestic lenders to Jet Airways have initiated the bidding process for sale of up to 75 per cent stake in the airline and the list of final bidders are expected to be known in the second week of May.
"I must also state that we have not yet given up on our efforts and continue to engage with the lenders and support them in the bid process. We are working with them proactively to find opportunities to revive our beloved airline," the communication said.