Now is a "dangerous time for Switzerland (but) unlike Luxembourg, Switzerland is not part of the EU" and it meets Organisation for Economic Cooperation and Development criteria, Maurer said in an interview published on Sunday.
Luxembourg, home to a prized financial centre, changed tack last Wednesday in the face of growing international pressure over tax evasion, agreeing to the automatic exchange of bank account information with its EU partners from 2015, he told the Swiss weekly Le Matin Dimanche.
Banking secrecy is "comparable" to medical confidentiality, Maurer said, adding: "The state must absolutely respect the private sphere" and should not know "what there is in your bank account".
Maurer said that Switzerland has already made concessions, noting that honouring the United States' Foreign Account Tax Compliance Act led to the lifting of banking secrecy for US customers of Swiss banks.
Moreover, "banking secrecy no longer has as much importance as two or three years ago," he said.
"The banking centre's strength also has to do with Switzerland's political stability, its reliability and its credibility."
Internal pressure, however, could force Switzerland to change position, he conceded.
When asked about wealthy foreigners who profit from Switzerland's banking secrecy practices to avoid taxes, Maurer said: "In each system there are ways to slip through the holes of the net. We must correct these flaws."
Maurer said that Swiss politicians have right to privacy just like other citizens of the country.
For that reason, he said, he was not in favour of Swiss government members having to disclose their assets, as is being proposed by the French government under President François Hollande.
Maurer said he was happy to make public his own assets.
Early in his career, he said, he did not earn much money and he has six children, of which three are still students.
"I have a house with a mortgage, and a car, a Subaru nine years old, and nine bicycles."
He added that he also had a "super" pair of cross country skis, "but I live simply".
Among other revelations, Maurer said he did not watch television and did not follow foreign news.
"I do not pass my time in front of the (TV) screen, I prefer to do sport."