Global authorities should dismantle banks that are so large their failure could destabilize the international financial system, Dallas Federal Reserve President Richard Fisher said on Wednesday.

While it's unclear exactly how big is too big, he said, links among the largest banks mean that the foundering of a few can lead to a downward spiral that destroys jobs and companies and creates enormous social costs. Creating a resolution authority to wind down large financial institutions that do fail could give false comfort to creditors who may see it as government backing, he said.

The point is there are limits to size and to scope beyond which global authorities should muster the courage to draw a very bright, red line, Fisher told a Levy Economics Institute conference in New York, adding that if the U.S. must act alone in order to break up too-big-to-fail banks, it should. The risk posed by coddling TBTF banks is simply too great.

Fisher's remarks come as U.S. President Barack Obama stepped up pressure on lawmakers to approve a Senate bill to tighten Wall Street regulation. The bill is drawing criticism from Republicans who argue its plan to create a resolution authority is an invitation to future bailouts, a claim the White House disputes.

I think the disagreeable but sound thing to do regarding institutions that are TBTF is to dismantle them over time into institutions that can be prudently managed and regulated across borders, Fisher said Wednesday.

Fisher also repeated his call to keep oversight of smaller banks under the Fed's purview. That authority would be stripped under recent Congressional proposals.

Here is the message for those who would peel away regulatory policy from the Fed: We depend on our regulatory arm to provide in-depth, hands-on assessments to guide us as we perform our duty as the lender of last resort, he said. Monetary policy depends upon regulation that ensures the soundness of financial institutions.

Central banks must also maintain their political independence to be effective, he said, citing Greece as a prime example. While in times past the country's leaders turned to the central bank to help inflate their way out of debt, he said, that's no longer possible in Europe.

The monetary authority is off-limits as an escape hatch, he said. And that is the way it should be --be that authority European or American.

(Reporting by Ann Saphir, Editing by Chizu Nomiyama)