NEW YORK (Reuters) - America's top financial regulator said on Tuesday "everything is up for a fresh look" as the Federal Reserve considers dialing back some crisis-era banking rules put in place over the last decade, offering hope to Wall Street and Republicans looking to cut red tape.

Randal Quarles, making his first public comments since becoming the Fed's vice chair for financial supervision this month, said there are some areas such as better tailoring rules to firms' size that can be adjusted immediately.

"As I have come into the job I have perceived quite an openness in the deep-state Fed to taking a fresh look, which I found very encouraging," he told a banking conference in New York, adding any regulatory changes ultimately "won't be to everyone's satisfaction."

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U.S. President Donald Trump and the Republican-controlled Congress aim to loosen requirements on banks and financial markets to free up capital flow and encourage economic growth. But Democrats, regulators, and Quarles' colleagues at the U.S. central bank, including Fed Chair Janet Yellen, have warned not to go too far in revamping rules and laws put in place to avoid a repetition of the 2007-09 financial crisis.

While stress-testing and capital standards for banks are necessary, the Fed should conduct these tests in a "simpler" and "much more transparent" way, said Quarles, who is also a Fed governor. Restrictions on leverage ratios should remain primarily as a "backstop" to financial stability, he added.

New risks such as cyber security breaches and the growth of financial technology could spark the next financial crisis, he said. "History has shown that it's not just a question of 'where has the risk that we knew moved to' but also what new risks are developing."

A year after Trump's election win, congressional attempts to peel back financial regulations have largely stalled, prompting bankers to look to regulators - and Quarles in particular given he was nominated by the White House - to loosen the reins through rule tweaks and more lenient supervision.

In a 25-minute question-and-answer session at the conference, Quarles added that the U.S. central bank does not need to wait for legislation and instead can "move right away" to better tailor rules to firms' sizes.

Without elaborating, he said the Fed would make a formal request for public input on a transparency proposal "in a very short period of time" - a promise that could encourage those on Wall Street anxious for deregulation to begin.

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(Reporting by Jonathan Spicer and Olivia Oran in New York; Editing by Lisa Shumaker)