According to the union, employees who have left have done so due to their financial condition and other commitments.
"We will not let this company go down and will not tolerate this casual talk to dismantle this company piece by piece and give it as doles to airlines of your choice," the letter said.
It also said that many employees have been with Jet Airways for 15-25 years.
"We have given our sweat, blood and tears to this company. Many of us who had left this company, have came back not once but twice and thrice," it added.
Bogged down by cash crunch, Jet Airways shuttered operations temporarily on April 17. Senior airline officials, including CEO Vinay Dube, Saturday met Finance Minister Arun Jaitley.
Dube said Jaitley had assured to look into the issues that forced the cash-strapped airline to halt operations temporarily.
Maharashtra Finance Minister Sudhir Mungantiwar, civil aviation secretary Pradeep Singh Kharola, the airline's chief financial officer Amit Agarwal, representatives of pilots, engineers, cabin crew and ground staff unions were also present at the meeting with Jaitley at his residence in Delhi.
Meanwhile, senior BJP leader Subramanian Swamy has suggested amalgamating Jet Airways with Air India.
"Govt better be careful: Two Ministers are manipulating sale of Jet Airways spoils to Spice Jet whose real owners I will reveal later. Only above board option GOI has is amalgam of Jet with Air India since Bilaterals on airspace involves Govt," he said in a tweet.
Lenders of Jet Airways have started the process for stake sale in the cash-strapped carrier.
SBI, the lead lender of the seven-member consortium of domestic banks that have extended loans to the airline, has started the bidding process for stake sale in the carrier and clarity about potential bidders would emerge next month.
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