The Federal Reserve should pare its bond buying as quickly as possible, even if doing so sends stock prices tumbling, because more bond buying risks inflation and makes an eventual exit from easy policies more difficult, a top Fed official said on Tuesday.

Richard Fisher, president of the Dallas Federal Reserve Bank and one of the Fed's most hawkish policymakers, said that continued purchases by the U.S. central bank of Treasuries and mortgage-backed securities carries the risk of fueling an asset price bubble, though he stressed that no such bubble now exists.

"Were a stock market correction to ensue while I have the vote, I would not flinch from supporting continued reductions in the size of our asset purchases as long as the real economy is growing, cyclical unemployment is declining and demand-driven deflation remains a small tail risk," Fisher said in remarks prepared for delivery to the National Association of Corporate Directors.

"I would vote for continued reductions in our asset purchases, with an eye toward eliminating them entirely at the earliest practicable date," said Fisher, who rotates into a voting spot on the Fed's policy-setting panel this year

The Fed is well into a second year of its third round of quantitative easing, the extraordinary measures known as QE3 which are aimed at pushing down long-term borrowing costs in order to boost hiring and growth.

Last month, nodding to a strengthening labor market, policymakers decided to trim the monthly purchases of U.S. Treasuries and mortgage-backed securities to $75 billion monthly, from $85 billion.

They also signaled they would likely end the purchases entirely later this year, but promised to keep interest rates low until long past that in order to continue to bolster growth.

U.S. stocks, which had risen throughout 2013, surged to record highs after the December decision, and continue to be at lofty levels that Fisher called "eye-popping" by some measures.

Fisher said he was pleased with the decision to begin reducing the program, though he would have preferred to slash it to $65 billion for starters so as to bring it to a close even faster. He has opposed the program from its beginning, saying it puts the nation at risk for inflation without being very effective.

The Fed's balance sheet has ballooned to $4 trillion with the cumulative purchases from its three bond-buying programs undertaken since the Great Recession.

Adding more to it is "untenable," Fisher said, because it risks fueling a rise in asset prices to unreasonable levels and complicates the Fed's eventual exit from super-easy policies.

While stocks, bonds and other assets are not currently in "bubble mode," he said, "one must be prepared for adjustments that bring markets back to normal valuations."

Janet Yellen, who takes over as Fed chief after Jan. 31 when Ben Bernanke's term ends, is expected to continue to pare the program and end it later this year, unless the economy takes a clear turn for the worse.

Fisher's comments suggest that he will keep up the pressure to do so, even if markets react unfavorably.

The tools the Fed will eventually use to tighten policy will likely result in smaller Fed payments to the Treasury and bigger Fed payments made to private banks to induce them to keep from flooding the financial system with too much cash and fueling inflation, he said.

His biggest concern, he said, is that Fed policymakers fail to remove stimulus fast enough because they fear criticism for creating such a situation.

"As soon as feasible, we should change tack," Fisher said in tones that were unusually strident even for the straight-talking Texan. "I plan to cast my votes at (Fed) meetings accordingly."

(Reporting by Ann Saphir; Editing by Leslie Adler)