The appeal comes on a day when the management of the airline is meeting the lenders.
As many as 1,000 pilots of the union, National Aviator's Guild (NAG), will meet on Monday morning to decide on whether the pilots will fly or not, due to non-payment of salaries. The debt-ridden carrier has also not paid the March salary to employees of other categories as well.
Also on Monday, Jet Airways pilots demonstrated in Mumbai after deciding against a strike, saying they had not been paid in four months and asking India's government for a lifeline. It also announced the resignation of one of its independent directors, Rajshree Pathy, from the company for other commitments.
Last month, Goyal and his wife Anita Goyal stepped down from the board of the airline, which has more than Rs 8,000 crore debt.
Goyal quit as chairman of the carrier last month under a debt resolution plan that saw lenders taking control of the airline.
The Guild has requested its members to be present at the airline's headquarters, Siroya Centre, in Mumbai's Andheri suburb at 9.30 am on Monday in their uniforms.
An urgent meeting to discuss the Jet situation was held at the prime minister's office on Friday, which was also attended by the country's aviation secretary, Pradeep Singh Kharola.
An Open House will be called shortly as per the availability of the venue and the committee members, the communication added.
The airline now has nearly its entire fleet of planes grounded for non-payment of dues amid a severe cash crunch. Further, it has closed reservations for its Mumbai-London, Mumbai-Amsterdam-Mumbai and Bangalore-Amsterdam flights, till April 18, according to the information.
A consortium of U.S. firm and Jet Airways founder Naresh Goyal's Jetair has reportedly submitted the expression of interest (EoI) for acquiring a stake in the ailing airline with the backing of a London company.
The beleaguered airline, which is flying just six-seven aircraft on Saturday, has asked its lenders to grant some "interim funding".
In a statement, Jet Airways said it has cancelled all worldwide flights until 18 April.