Altman: 5.5% jobless not telling true labor story

The Federal Reserve better not rush to increase interest rates in June because the labor market is really weaker than it appears, former Deputy Treasury Secretary Roger Altman said Thursday.

"I don't think 5.5 percent [unemployment rate] is the best measure of labor market conditions," the former Clinton administration official said in a CNBC "Squawk Box" interview.

Last Friday, the government said the jobless rate fell to 5.5 percent for February, while nonfarm payrolls growth boomed by 295,000, despite the brutal winter conditions.

Read MoreSurge! Job creation jumps despite tough winter

"If 5.5 percent were really capturing the conditions, you wouldn't see wage growth just barely ticking up," said Altman, founder of Evercore Partners. American worker pay rose just 3 cents an hour for last month, representing a 2 percent annualized gain.

Wage inflation remains low, as do consumer and producer inflation. Fed policymakers have repeatedly said they want to see more pricing pressures before raising rates.

The Fed started cutting rates to their current near zero percent levels in 2007 and 2008. The last Fed funds rate hike was in 2006.

Acting in June or September does not really matter in the greater scheme of things, Altman said. But it's important to act at some point, he argued, to give the Fed another weapon besides bond purchasers to fight future crises. "One of the downsides of QE ... is we don't have anything left in the toolbox if there should suddenly be a crisis. And often crises come out of the blue. The next one never comes where the last one came from."

With U.S. central bankers on the verge of tightening and the European Central Bank just embarking on bond purchases amid an extremely low rate environment, Altman said it's no surprise the euro has been so weak.

The euro early Thursday was higher against the dollar for the first time in two weeks, recovering from a 12-year low hit overnight.

"This fall in the euro is going to have a really strongly stimulative effect," Altman said, pointing to the euro zone's more export-driven economy compared to the U.S. But that's not going to immediately help Europe, he added. "I personally think it's going to be a long, slow road for European recovery."

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