Minneapolis Fed president Neel Kashkari said Tuesday he is still not ruling out an interest rate hike, but it’s more likely the central bank could hold rates steady for an "extended" time as it waits for inflation to drop.

"We could sit here for as long as necessary until we get convinced that inflation is sustainably going back down to our 2% target," he said.

While holding rates at their current 23-year high "for an extended period of time is a more likely outcome," Kashkari made it clear that other options are on the table if inflation doesn't fall.

Read more: What the Fed rate decision means for bank accounts, CDs, loans, and credit cards

"I'm not ruling out potential interest rate increases from here," he said.

Kashkari is the latest of many Fed officials to stress a stance of holding rates steady for longer in the weeks following the last Fed meeting that ended May 1.

The Fed decided on May 1 to keep its benchmark interest rate in a range of 5.25%-5.50% as it tries to get inflation down to its goal of 2%.

Minutes from that meeting released last week indicated some policymakers discussed their willingness to raise rates if needed.

"Various participants mentioned a willingness to tighten policy further should risks to inflation materialize in a way that such an action became appropriate,” according to the minutes.

Hopes for a rate cut this year are dwindling. Investors have now scaled back the odds of the potential first rate cut in September, with a 50% chance the Fed won’t cut rates that month. Odds of a cut in November are 46%.

The inflation readings in the first quarter were hotter than expected, but an April reading released after the Fed's last meeting did show some easing of those price pressures.

The Consumer Price Index on a "core" basis, which strips out food and energy prices, rose 3.6% year over year, a cooling from the 3.8% increase seen in March.

This Friday officials will get a fresh reading from their preferred inflation gauge, the Personal Consumption Expenditures index on a core basis, which strips out volatile food and energy prices.

Economists expect April's "core" PCE clocked in at an annual gain of 2.8%, flat from March's increase.

Over the prior month, economists expect "core" PCE rose 0.2%, down from 0.3% the month prior.

Until Fed officials are convinced that inflation is actually coming down, Kashkari says he could see the Fed sitting with rates at current levels for an indefinite period of time, noting that the lags of monetary policy potentially are longer than anticipated.

But “we might also conclude policy is actually not restrictive enough— the disinflationary process is not on its way — and therefore that would be the situation where we would potentially have to go up again."

"I don't think it's very likely, but I can't rule it out," he said.

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