Roughly 15 Swiss banks are in a "red zone" of lenders particularly exposed to money laundering risks, the head of Swiss banking watchdog FINMA said in a newspaper interview published on Sunday.

Swiss federal prosecutors last week said that they have opened criminal proceedings against Zurich-based Falcon Private Bank for alleged failure to prevent suspected money laundering linked to Malaysia's scandal-tainted 1MDB fund.

Falcon is the second Swiss bank, after BSI, to face a criminal investigation by Switzerland's Office of the Attorney General over links to 1Malaysia Development Berhad (1MDB). The move is partly based on an investigation by FINMA, which has also opened proceedings against several other lenders.

"We have introduced a warning system in relation to money laundering risks," FINMA Chief Executive Mark Branson said in an interview with Swiss newspaper SonntagsZeitung. "Roughly 15 banks are in the red zone here. That means they are particularly exposed."

Branson did not name the banks concerned but said that most of them are involved in asset management and often have clients from emerging markets, adding that the lenders were from all areas of the country and of various sizes.

Asked whether any major Swiss banks were among them, he said: "I would not use the plural, but yes."

Banks on the list are monitored more closely and must provide FINMA with additional information, but the watchdog wants them to understand the emerging markets in which they operate rather than withdraw from them, Branson said.

Falcon, which FINMA has ordered to turn over 2.5 million francs ($2.56 million) in what the watchdog said were illegal profits, is being given a second chance but would lose its banking license in the event of a repeat offence, he said.

"Falcon was a hair's breadth away from having its license withdrawn," Branson said. "We are of the opinion that the new management deserves a chance."

Some banks are increasingly willing to take risks in relation to money laundering as they come under growing economic pressure to find new clients, Branson said, but banks have also reported more suspicious cases in recent months.

In addition to investigations linked to 1MDB and a separate scandal involving Brazil's state-controlled oil producer Petrobras (PETR4.SA), Branson said that FINMA is investigating an unnamed Swiss bank in relation to FIFA, the world soccer governing body mired in corruption probes.