'If an alternative resolution is not reached, the Department of Justice will continue to vigorously pursue enforcement of the summons through the court,' it read.
Reports in the Swiss media have suggested UBS might hand over some names, probably of clients who were involved in some form of tax fraud, if it could get a guarantee that the case would then be closed.
A spokesman for UBS declined to immediately comment saying the bank would release a statement later Sunday.
In February, one day after UBS admitted wrongdoings, handed over information on a reported 250 clients and agreed to pay 780 million dollars in fines, the US launched the new demand for more data. The bank's employees are said to have helped wealthy clients evade paying their taxes.
Switzerland is in the process of renegotiating its double-taxation agreements with various governments, including the US, in order to get off the Organization for Economic Cooperation and Development's so called 'grey list' of countries without sufficient disclosure.