Cleveland Federal Reserve President Loretta Mester told CNBC on Friday the government's weaker-than-expected employment report for September was still strong enough to keep her thinking central bankers should increase interest rates.

"It's a solid labor market report," Mester said on "Squawk Box." She's a voting member this year on the Fed's policy panel, the Federal Open Market Committee. "This is very consistent with what we expected to see."

"The economy has been very resilient," she said, citing bounce backs from the stock market plunge early in the year and the June vote by Britain to leave the European Union.



On Friday morning, the Labor Department said 156,000 nonfarm jobs were added in September. The unemployment rate rose slightly to 5 percent. "The unemployment rate is about at what my estimate of full employment is, natural rate of unemployment," Mester said.

Economists polled by Reuters had predicted the U.S. economy would create about 175,000 nonfarm payrolls last month, with an unchanged jobless rate of 4.9 percent.

"Remember 75,000 to 120,000 [jobs added] per month is about what you need to keep unemployment stable," Mester said, citing stronger labor market numbers this year, with the three month average of about 192,000.

Average hourly earnings matched expectations with an increase of 0.2 percent in September and an annualized rate of 2.6 percent. The average work week also inched up one-tenth to 34.4 hours.

"I see inflation measures moving up," in addition to stronger jobs, Mester said. "We have to be forward-looking. So in terms of our two goals ... it makes sense to move up the [fed funds] rate another 25 basis points."

The Fed's next two-day meeting concludes on Nov. 2, just six days before the presidential election. But Mester said "all meetings are on the table" for a possible rate increase, and that politics do not have any bearing on policy setting decisions.

The Fed also meets in December, one year after the Fed hiked rates for the first time in more than nine years.

"I don't think we're behind the curve yet. I don't see that we need to bring rates up very quickly," Mester said. "I'd like to be on this gradual path that we've been communicating."