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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 More Surge! 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 (EVR). 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.

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