KBC Bank has made the application, which is currently owed around €75m by Treasury in loans and guarantees given to Treasury companies.
Treasury went on record saying that 300 jobs are at risk and the companies should be given more time to negotiate with potential investors.
The Convention Centre Dublin is one of the developments affected by the case.
KBC Bank was part of a syndicate which lent around €300m to Treasury companies for developing Spencer Dock.
KBC insists that Treasury and related companies is wound up and a liquidator to be appointed.
Treasury says KBC cannot act without the other member of the syndicate, which is now NAMA, and asked the court to use its discretion to adjourn the winding up petition for a number of weeks to allow further discussions with potential investors to take place.
Treasury suggested KBC would not be prejudiced by an adjournment and had an ulterior motive for seeking to have the companies wound up.
Treasury said if the companies were liquidated, a decision about appealing a High Court decision rejecting its challenge to NAMA’s decision to call in its loans would be taken out of the hands of the Treasury directors.
Lawyers for KBC Bank said the companies were wholly insolvent and were looking for some kind of quasi court protection.
Senior Counsel Lindon McCann said Treasury had made continued and protracted efforts to do anything but repay the loans.
He said Treasury was hoping a white knight would come along to take over the loans but they had been looking for this white knight for months and months.
He said all KBC Bank wanted was to be paid.
He said a new offer to take over the loans from Morgan Stanley involved KBC and NAMA providing finance to Morgan Stanley to buy the loans and was commercially unattractive.
The case will continue tomorrow.