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Fed's Williams: Jobs report shows 'good momentum'

Fed's Williams: Labor market improving
Fed's Williams: Data dependent strategy appropriate
Fed's Williams: We watch financial stability carefully
After a rebound in US jobs, will Fed raise rates?

Recent jobs data show "good momentum" for the rest of the year, San Francisco Fed President John Williams told CNBC on Monday.

Last week, the Labor Department announced that the U.S. economy had created 223,000 jobs in April and that the unemployment rate had touched a seven-year low of 5.4 percent, but wage growth only rose slightly from March.

Some economists have said the results of Friday's jobs report will not be strong enough to cause the Federal Reserve to raise rates soon.

Read MoreWilliams' predictions in January: 3% growth and more

Williams, a voting member of the Federal Open Market Committee, said on CNBC's "Squawk on the Street" he is seeing progress on the employment front but the "real question" is whether inflation is where the Fed wants it to be. He cited the strong dollar among other factors holding inflation below the 2 percent target.

The San Francisco Fed president said his personal one-year forecast indicates that the U.S. economy will see unemployment below 5 percent, underemployment at "more normal levels," inflation heading back to 2 percent, and "rates will be moving up."

John Williams holds a T-shirt on CNBC's "Squawk On the Street," Monday, May 11, 2015.
Source: CNBC

When asked about the prospect of a near-term rate hike, Williams brandished a T-shirt that read "Monetary Policy It's Data Dependent." (Williams said he had distributed the shirt to some of his colleagues.)

The Fed is better off not signalling a rate hike much in advance so it can more heavily rely on economic data, he said. In fact, Williams explained, a rate hike is on the table at every FOMC meeting.

The U.S. gross domestic product figure, he said, will likely rebound in the second quarter from weakness at the beginning of the year.

"I think that GDP number in Q1 is more an anomaly than a signal of where the economy is going," he told CNBC.

Read More Yellen says equity valuations generally high

Turning to equity markets, Williams said he agreed with recent comments from Fed Chair Janet Yellen that equities valuations are high, but he is not worried about the issue.

"I really see this as being more of a reflection of where globally long term rates are and returns are, and that pushes stock market[s] up and other financial markets up," he said. "I'm not overly concerned about threats to financial stability out of this, but it's definitely something we watch carefully."

Williams added that one of the lessons the Fed learned from the financial crisis is that it should monitor developments in financial markets around the world.