The Fed's Neel Kashkari says the central bank has not made enough progress to keep its rate outlook

Minneapolis Federal Reserve President Neel Kashkari said Tuesday that the sharp job growth in January was evidence that the central bank has more work to do to tame inflation.

That means continuing to raise interest rates as they see the likelihood that the Fed's benchmark borrowing rate should rise to 5.4% from the current target range of 4.5% to 4.75%.

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

Kashkari spoke just days after the Labor Department reported that nonfarm payrolls rose by 517,000 in January, nearly triple Wall Street's expectations and the strongest first-month gain since 1946.

The strong job growth came despite the Fed's efforts to use higher interest rates to correct what officials called a "mismatch" in the labor market between supply and demand. There are nearly two job openings for every available worker, and average hourly earnings rose 4.4% in January from a year earlier, a pace the Fed considers unsustainable and inconsistent with its 2% inflation target.

The data "tells me that so far we don't see a big footprint on the labor market from our tightening to date." There is some evidence that it's having some effect, but it's pretty muted so far," Kashkari said.

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

Kashkari's hint that the Fed Funds rate must rise to 5.4% puts him in a more aggressive slot compared to his fellow policymakers, who said in December they see a "tail rate," or end point, of hikes around 5.1%. The funds rate is what banks charge each other for overnight lending, but it is factored into many consumer debt instruments such as car loans, mortgages and credit cards.

Kashkari is a voting member of the rate-setting Federal Open Market Committee this year.

Since March 2022, the Fed has raised its benchmark funds rate eight times after inflation hit its highest rate in more than 40 years. The latest increase came last week with an increase of a quarter of a percentage point, the smallest since the first move.

Along with the rate hike, the central bank allowed up to $95 billion a month in bond yields to draw down its balance sheet, resulting in another nearly $450 billion in tightening.

However, the level of inflation, while easing, is well ahead of the Fed's target, and policymakers have indicated that more rate hikes are on the way.

"I don't see us making enough progress yet to declare victory," Kashkari said.