While a rate hike in June is "possible," Kashkari sounded happy to keep rates low for now in order to continue bringing workers who have not worked in months or years back into the labor force.

"To me, just looking at the raw data, it says we should be accommodative, and I think we have this other societal need that we should be accommodative, because if we can keep people from being lost permanently, boy that's a real positive for society," Kashkari said in an interview in his bank's cafeteria overlooking the Mississippi River.

Kashkari said the U.S. economy is likely to grow at about a 2-percent pace this year.

He said it was not clear whether a recent pick-up in inflation was "real" or due to transitory factors.

Until there is good evidence inflation is moving toward the Fed's 2-percent target, "I feel like we have the luxury of allowing the labor market to continue to bring people back into the workforce," Kashkari said.

At the same, Kashkari did not rule out the possibility that wages, the unemployment rate, labor force participation and the inflation outlook could improve enough before June for the Fed to raise rates then.

"It's possible," Kashkari said. "I don't want to prejudge."

Kashkari has been an outspoken critic of the Fed's and other regulators' approaches to overseeing big banks, saying they don't go far enough to prevent future bailouts.

Kashkari's first detailed remarks on monetary policy since becoming president of the Minneapolis Fed in January, however, signal the former Republican candidate for California governor backs Obama-appointed Yellen fully on the interest-rate front. Presumptive Republican presidential nominee Donald Trump said he probably would replace Yellen when her term is up in early 2018.

"I am not going to comment on any of the presidential candidates or their policy proposals, other than to say I think Chair Yellen is doing a terrific job and whoever the next president is should reappoint her," Kashkari said.

Encouraged by a strengthening labor market, Fed policymakers raised rates in December for the first time in nearly a decade. But since then they have stood pat, worried by a slowdown in China and Europe that has hampered growth and inflation at home. In March, Fed officials slashed their expectations for rate hikes this year to just two, from four in December.

The Labor Department reported on Friday that U.S. employers added 160,000 jobs in April, short of the 202,000 expected by economists and below the recent monthly average of 200,000, tempering hopes of a strong economic rebound in the second quarter.

Even as Wall Street economists all but gave up hope for a June rate rise after the report, the influential head of the New York Fed repeated his view that two interest rate hikes this year were still a "reasonable expectation."

Kashkari said he did not see any advantage to advertising his preference for a certain number of rate hikes this year.

"If we make a forecast of the number of rate hikes and then we change it, everybody freaks out," he said, adding that the decision will "totally depend on how the economy performs."

The Fed can only do so much to telegraph its intentions on policy, Kashkari said. Markets are currently pricing in just an 8 percent chance of a June rate hike, and don't see better-than-even odds of a Fed move until December.

"At the end of the day we are going to react to the data, and if the data surprises to the upside, then the markets will have to adjust," he said.

The Fed needs to focus on economic data, and not worry so much about uncertainty in an election year and what the market expects it to do.

"There's always uncertainty.There are lots of reasons not to do anything, and then you get stuck in a place where you are just, you are afraid to do anything," he said. "We need to look at the economy and do what's right for the economy based on what the data is telling us, and markets will adjust."