NEW YORK (CNNMoney.com) - Prices paid by consumers for goods other than food and energy rose more than expected in May, making it all but certain the Federal Reserve will raise interest rates at least one more time.

The Consumer Price Index, the government's main inflation gauge, posted a 0.4 percent rise in May after jumping 0.6 percent in April, the Labor Department reported Wednesday. That was in line with forecasts of economists surveyed by Briefing.com.

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But the even more closely watched core CPI, which strips out often volatile food and energy prices, rose 0.3 percent, the same rise seen in April. That April report helped spark a sell-off in worldwide stock markets that's persisted for most of the last month. Economists had forecast only a 0.2 percent increase in May.

The report helped settle the debate that's been roiling markets around the world, economists said.

"Now it's a unanimous view the Fed is going to raise rates on June 29," said Anthony Chan, chief economist for JPMorgan Private Client Services. "That debate is over."

More rate hikes from the Fed will raise the cost of borrowing for many consumers on credit cards and home equity loans, and are likely to cause businesses to curb spending as well, slowing economic growth and squeezing corporate profits.

That's why stock investors have been nervous about rising inflation and rates.

But stocks actually rallied Wednesday morning as investors welcomed some clarity about what would happen to rates. On Tuesday stocks fell for the seventh time in the last eight sessions, declines that had wiped out the market's gains for the year.

"I think we've become extremely oversold," said Art Hogan, chief market analyst at Jefferies & Co. "Today's inflation report certainly isn't a reason to get back into the market, but there are those who say that at some point we have to bottom out."

Hogan said the report could also reduce the pressure on Fed officials to give repeated statements as they have in recent weeks about the dangers of inflation, comments seen as signals that a June 29 rate hike was likely.

"We've had hawkish statements that have certainly roiled markets," he said.

While stocks rose, Treasury prices fell, lifting the yield on the benchmark 10-year note to 5.03 percent from 4.97 percent just before the report as bond investors bet rates are headed higher. Bond prices and yields move in opposite directions.

This month's CPI report was considered especially important as the Fed has said future rate hike decisions will depend on economic numbers.

The numbers show that core CPI now is up 2.4 percent over the last 12 months, well above the 1 to 2 percent target traditionally seen as within the Fed's comfort level.

The report showed that prices overall are now up 4.2 percent over the last 12 months, more than the seasonally adjusted 4 percent rise in average hourly wages over the same period, according to a separate government report.

That means that average workers' paychecks aren't keeping up with inflation. Perhaps more importantly, it is likely to spur the Fed to raise interest rates further than many investors hoped as recently as the beginning of the month.

The CPI reading is also the last major inflation gauge that will be released before the central bank's two-day policy meeting on June 28-29. (For more on what else the Fed will be looking at, click here).

In its report, the department said energy contributed to the rise in retail prices, jumping 2.4 percent last month, though that was less than the 3.9 percent gain in April.

But most other major price categories showed relatively modest gains. Housing prices and medical care both rose 0.3 percent in the month, and transportation costs, which include energy, climbed 1.5 percent. But other broad categories listed in the report posted modest gains of 0.2 percent or less.

At the Chicago Board of Trade, fed fund futures, which track investors' bets on Fed rate hikes, were indicating investors expect a 100 percent chance of a June rate hike, up from 86 percent Tuesday.

And investors upped their bets for an August rate hike as well. The futures contracts showed investors had been betting on a 64 percent chance of an August hike Tuesday, but that was up to 75 percent Wednesday morning.

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