Core inflation continued to be benign in May, rising 0.2% in the month and 2.3% in the year, but the Fed will likely put more focus on total inflation as that figure came in higher than anticipated, economists said on Friday after the CPI report.

Eric Lascelles, senior economics and rates strategist at TD Securities, said the report "didn't come in widely different" from expectations, but he said it will still rile the markets "given the incredible focus on inflation right now."

The all-items headline figure increased 0.6% (0.649%) month-over-month, a tenth higher than expectations and contributing to an annual increase of 4.2%.

Lascelles said headline index rose from broad-based gains, with gas up 5.7%, tobacco up 0.8%, housing up 0.5%, education up 0.4%, and commodities up 0.9% in the month. "There's not a lot of softness here," he said.

Although annual core inflation remains above the Fed's unofficial comfort zone, the monthly change was relatively benign in May, but it can no longer be said that core is the exclusive focus of the Fed, Lascelles added. He said the Fed began suggesting they were shifting some focus to total inflation back in the Fall when they started adding forecasts for headline inflation into the mix.

TD Securities expects "continued hawkishness on inflation by Federal Reserve officials, which suggests that the Fed is indeed on hold and that the next move for the Fed could indeed be a rate hike, rather than a rate cut."

By contrast, Ian Shepherdson, chief U.S. economist at High Frequency Economics, said "Rate hike makes no sense," arguing that "all the 'inflation' is in the headline," which he said was pushed up by oil, fuel, and utilities.

He said the trend is flat in goods prices excluding food and energy, apparel costs are down 0.3% in the month, cars are down 0.1%, and primary rents are slowing too.

Lascelles also voiced concern about the idea that downside risks have diminished, noting that while growth has been looking better recently, much of the data has been boosted by the fiscal stimulus package, which can only offer temporary benefit rather than fundamental changes.

Energy prices rose 4.4% in May, but are up 17.4% on the year, while gas rose 5.7% in the month and 20.8% in the year.

Before the release, BMO senior economist Sal Guatieri said, "With Bernanke & Co. on heightened alert for signs of creeping inflation, the consumer price report takes on added importance. An upside surprise here, coupled with yesterday's strong retail sales report, could see the Fed shift to a mild tightening bias on June 25."

"The continued high headline rate is starting to seep into inflation expectations, and a further increase is something Bernanke said he would strongly resist. While core inflation remains trendless, an upward drift could also force the Fed to walk the talk, despite lingering growth and credit market risks," he added.

By Patrick McGee and edited by Cristina Markham