WASHINGTON (Reuters) - A U.S. bank regulator is considering a stricter framework for how large asset managers like Blackrock and Vanguard can prove they are not influencing banks where they hold large stakes.

The Federal Deposit Insurance Corporation voted on Tuesday to advance a proposal that would see the agency exert more influence over whether asset managers or other firms building large stakes in banks should receive stricter regulation and oversight.

Agency officials also indicated they may launch a review of existing so-called "passivity agreements" with large asset managers, with a focus on boosting FDIC oversight of their commitments to not play an active role in bank management.

Under law, third parties that obtain a greater than 10% stake in a bank can be considered a controlling interest in the bank and subjected to stricter regulation and oversight. But firms can avoid those restrictions under so-called "passivity agreements," in which the investor commits to regulators they will not exert influence on the bank.

Specifically, under the proposal the FDIC would remove an existing exemption in which the agency does not review new large investments in banks, so long as the Federal Reserve signed off on that approach.

"It is highly inappropriate for the FDIC to abdicate the responsibility Congress entrusted to us to safeguard the ownership and control of the banks we supervise," said Rohit Chopra, director of the Consumer Financial Protection Bureau and an FDIC board member.

FDIC Chairman Martin Gruenberg also backed the proposal, which would also seek broader feedback about the role of asset managers obtaining large stakes in banks.

Separately, FDIC Commissioner Jonathan McKernan offered a proposal that would have directed FDIC staff to order a review of existing passivity agreements for some large asset managers, and ensure the FDIC has the capacity for monitoring the commitments those firms make. Under his plan, the FDIC would look to strike new agreements with those firms that would do away with the current practice of self-certification by the firms and require FDIC monitoring.

However, McKernan did not bring that proposal up for a vote after Gruenberg indicated such action would not require formal board action. Gruenberg added he is open to reviewing existing agreements, with a focus on ending the practice of self-certification.

When asked, Gruenberg said he expected notifications to begin review existing agreements could happen soon.

The FDIC action comes amid growing concern among some policymakers over large asset managers' expanding footprint in the banking sector, driven by the growth of index investing, and what it could mean for bank management. In his remarks, Chopra noted BlackRock and Vanguard collectively control over $17 trillion in assets, with stakes large enough to trigger stricter oversight.

A spokesperson for Blackrock declined to comment. Vanguard said in a statement it wants a "constructive dialogue" with regulators over passive investments.

Spokespeople for those firms did not immediately provide comment on the FDIC's actions.

But the industry has been quick to critique this scrutiny, calling it unjustified and burdensome.

"It is alarming to see that the FDIC is proposing to revise the current framework in the absence of a clearly identified problem," said Eric Pan, CEO of the Investment Company Institute, which represents asset managers. "We fear that the FDIC is asking the investment funds industry to prove a negative, setting up a flawed foundation on which to impose harmful limits and red tape on investment funds and increase costs on American investors."