WASHINGTON (Reuters) -A leading U.S. bank regulator proposed rules Tuesday that would limit how bank examiners can police and address shortcomings within lenders, as the Trump administration continued efforts to rein in supervision the banking industry has long complained is overly punitive.

The Federal Deposit Insurance Corporation approved a pair of proposals that would direct its examiners to focus on core financial issues, and restrict their ability to police nonfinancial matters.

The first proposal, approved by the Republican-led panel, would define "safety and soundness" for banks as any issues that pose a material financial risk to the institution. Specifically, the proposal would limit the use of so-called "matters requiring attention," where a regulator orders a bank to address problems, and other enforcement actions to issues that have caused or could cause significant financial harm to the bank or make it more likely to fail.

Travis Hill, the acting head of the regulator, said examiners would still be able to proactively identify potential problems, but their focus needed to be refined to core financial matters instead of "a litany of process-related items."

The second proposed rule would codify a practice already adopted by the Trump administration, which has scrapped the use of so-called "reputation risk."

All three major U.S. regulators announced earlier this year they would no longer apply that standard, which is when firms engage in activities that have the potential for negative publicity to hurt a bank's business or lead to costly litigation. Hill said in a prepared statement that this standard is "ripe for abuse" and "adds no value" to supervising banks. The proposal also would bar examiners from steering banks to avoid providing any services on political, social, cultural or religious views.

The industry had pointed to that standard as a common culprit in cases of "debanking," when businesses or individuals claimed they were denied banking services on political or similar grounds. President Donald Trump signed an executive order in August explicitly barring the supervisory practice.