The pilots gave the ultimatum at a meeting with top management representatives including chief executive Sanjay Agarwal.
In a bid to pre-empt legal action by the engineers, the management of Vijay Mallya-owned carrier appealed to them not to take such a step but did not make any commitment about the payments, sources said.
"The management has appealed to the engineers to not file a winding-up petition as it will have an adverse impact on the revival plan, which is awaiting regulatory approval," airline sources told PTI.
The appeal was made at a two-hour meeting between the management and pilots at the Kingfisher House here this evening.
In New Delhi yesterday, the engineers had decided to move a winding-up petition in the Delhi High Court by the end of the week.
"Pilots categorically told the management that it must clear their salary dues by the month-end failing which they will take a legal recourse in the form of a similar action that is decided by the engineers," sources said today.
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The management, however, told them that it expects to have "some funds in the account" by the week end, the sources said.
"Chief Executive Sanjay Aggarwal, along with Executive Vice President Hitesh Patel, attended the meeting, but did not make any commitment to make the payments," they said.
According to sources, pilots also demanded a "written assurance" from Mallya through an e-mail about clearing their dues by January 31.
"However, Agarwal did not make any assurance," they said. More