By Pete Schroeder

WASHINGTON (Reuters) -The head of the Federal Deposit Insurance Corporation said Thursday that bank regulators are considering applying an upcoming set of stricter capital rules to banks with over $100 billion in assets.

FDIC Chairman Martin Gruenberg said in a speech the spring turmoil in the banking sector showed firms of that size pose a risk to the financial system and merit stricter oversight. Three banks failed during the spring, requiring regulators to step in and backstop deposits.

"If we had any doubt that the failure of banks in this size category can have financial stability consequences, that has been answered by recent experience," he said in prepared remarks. "The lesson to take away is that banks in this size category can pose genuine financial stability risks."

He added agencies will propose new capital rules to implement an international bank rule agreement in the near future, but will likely not complete the rules before the middle of 2024.

The so-called Basel III "endgame" rules are already a focus of intense criticism by the banking industry, who are arguing to regulators and lawmakers that overly strict requirements could hinder banks and the broader economy.

But Gruenberg argued it was critical, particularly in the wake of the spring bank failures, for regulators to get tougher rules in place.

"A robust regulatory capital framework is the cornerstone of a resilient banking system," he said, adding that the upcoming proposal "offers us the opportunity to make important modifications to the risk-based regulatory capital framework with the ultimate goal of enhancing the financial resilience and stability of the banking system, better enabling it to serve the U.S. economy."

(Reporting by Pete Schroeder, Editing by Nick Zieminski)