Richard Fisher, president of the Dallas Federal Reserve Bank, said the United States risks falling behind the curve on inflation as wage pressure starts to bubble in some parts of the country.

"I think we could suddenly get a patch of high growth, see some wage price inflation," Fisher said on the Fox news program Sunday Morning Futures with Maria Bartiromo. "I'm not worried about it yet, but I've seen it in my own federal reserve district and I think it could happen to the nation as a whole."

Fisher said the U.S. economy was "definitely pulling ahead of the rest of the world" and that "our wounds have been healing".

Some areas, such as Texas, have seen explosive growth, he said. The state benefits from a diversified economy and a pro-business government that has lead to job growth and "massive immigration".

"We were creating jobs in the second quarter at a rate of 5.8 percent, way ahead of the nation," he said. "If the federal government would only get their act together and be more like us we would be growing as a nation much, much faster."

That growth was being accompanied by wage pressure, he said.

"We're seeing wage price pressures in our surveys that are the highest since before the recession in my federal reserve district," he said.

The Federal Reserve has said it plans in October to end its third round of "quantitative easing" -- a tool used to stimulate the economy. The question, Fisher said, was "how quickly we move to normalize interest rates".

Fisher has previously said he expected interest rate hikes to come "sooner rather than later" and on Sunday he said he was worried that "we are behind the curve at the Fed".

"Monetary policy works with a big lag," he said. "I don't want to fall behind the curve here."

He also warned people to be prepared for when rates do rise.

"We've been fueling the markets, and at some point trees do not just grow to the sky," he said.

Fisher is a voting member of the Fed's policy-setting body in 2014 and is seen as one of its most hawkish members. Other Fed officials worry that tightening policy too soon could derail the U.S. recovery and risk deflation.

William Dudley, head of the powerful New York Fed, said recently that "we need the economy to run a little hot for at least some period of time to push inflation back up to our objective".

Inflation unexpectedly cooled in August and is falling short of the Fed's 2 percent target.