A top banking regulator said it would for the first time allow financial-technology firms to apply for federal charters, a move that will give the rapidly growing industry a new opportunity to expand while increasing government oversight of the sector.

"It will be much better for the health of the federal banking system and everyone who relies on these institutions, if these companies enter the system through a clearly marked front gate, rather than in some back door, where risks may not be as thoughtfully assessed and managed," Thomas Curry, the head of the Office of the Comptroller of the Currency, said in remarks prepared for delivery Friday morning at Georgetown University Law Center.