Such a council would be independent of governments and have the power to help countries implement economic reforms, if need be by determining where financial aid from fellow members would best be spent, Rösler told reporters.
"A stability council wouldn't mean -- 'you're not getting any money', but
rather we'll apportion it for you," said Rösler, who is also vice-chancellor in Angela Merkel's centre-right coalition.
Rösler, the head of the small pro-business Free Democrats (FDP), also called for "competitiveness tests" to determine how countries were managing their finances.
When a country failed such tests, "there would be consequences," he said.
He also urged eurozone countries to adopt "as quickly as possible" constitutional amendments to limit overall public debt.
Speaking against a background of growing international financial turmoil, Rösler said eurozone members should strive to adopt "a common culture of (financial) stability" and so limit the risks of debt contagion.
The minister, whose party has been outspoken in its criticism of debt-ridden countries such as Greece, said he would present his ideas next month at a European level.
Germany has long sought closer eurozone economic governance rules, arguing that tighter controls would prevent the sort of debt problems now besetting the 17-nation bloc.