Luxembourg, which has come under pressure over its role as a tax haven, must step up cooperation with its peers to protect the right of client confidentiality, Frieden said on Tuesday.
He made the remarks after meeting with Swiss President Eveline Widmer-Schlumpf, who is also Switzerland's finance minister.
"We need to step up coordination with other financial centres and come to a common understanding on client secrecy," Frieden said.
At the same time, they would also have to meet "indispensable and absolutely necessary" standards of honesty on tax matters, he added.
"It is all about better protecting the privacy of clients," he said, speaking alongside the visiting Widmer-Schlumpf.
Financial centres such as Luxembourg and Switzerland have been on the defensive since the global financial crisis in 2008 on charges that their secrecy laws made money flows harder to track, so enabling tax evasion.
Increased cooperation now should go beyond the issue of privacy since "there were other regulatory initiatives which we we need to come together on," Frieden said.
"In a crisis, many states looked only to their national markets," he said.
"We need to show that international financial centres are needed."
Clients now come to Luxembourg or Switzerland not for secrecy or tax avoidance but to benefit from the financial services they provide, he said.
Widmer-Schlumpf made a similar point.
"We work with money that has been notified to the fiscal authorities and we should build our business model on the . . . quality of our financial services."
Frieden noted that he had just begun talks with the US authorities so as to comply with the Foreign Account Tax Compliance Act (FATCA) which allows for an exchange of information on the assets of US citizens living abroad.