Minneapolis Federal Reserve President Neel Kashkari said Tuesday that explosive jobs growth in January is evidence that the central bank has more work to do when it comes to taming inflation.

That means continuing to raise interest rates, with the likelihood that the Fed's benchmark borrowing rate should rise to 5.4% from its current target range of 4.5%-4.7%.

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"We have a job to do. We know that raising rates can put a lid on inflation," Kashkari told CNBC during a Tuesday morning interview on "Squawk Box." "We need to raise rates aggressively to put a ceiling on inflation, then let monetary policy work its way through the economy."

Kashkari spoke just a few days after the Labor Department reported that nonfarm payrolls grew by 517,000 in January, nearly triple the Wall Street expectation and the strongest growth for the first month of the year since 1946.

That came despite the Fed's efforts to use higher interest rates to correct what officials have termed "imbalances" in the labor market between supply and demand. There are nearly two open jobs for every available worker, and average hourly earnings rose 4.4% in January from a year ago, a pace the Fed considers unsustainable and inconsistent with its 2% inflation goal.

The data "tells me that so far we're not seeing much of an imprint of our tightening to date on the labor market. There's some evidence that it's having some effect, but it's pretty muted so far," Kashkari said.

"I haven't seen anything yet to lower my rate path, but I'm obviously keeping my eyes open and we'll see how the data comes in," he added.

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