Gradual Rise in Rates Won't Stop Housing Recovery: Lennar

The housing recovery is on a normal trajectory and gradual increases in interest rates won't slow it down, Lennar CEO Stuart Miller told CNBC on Wednesday.

Miller, whose company is one of the nation's largest homebuilders, said the notion that the most recent Case-Shiller report signals a growing bubble in housing is a "knee jerk" reaction by the investment community. He said the housing recovery is behaving as it should.

With interest rates at historic lows, Miller expects that as rates move up, slight increases "are not going to stop the progress forward" of the housing recovery.

(Counterpoint: Rising Mortgage Rates, Home Prices a Lethal Brew)

"Housing continues to find its rebound and gain strength," he said. "Over the past five years we have under-constructed for a growing household formation that has been stymied by economic downdrafts."

Miller estimates that the country needed 1.25 million to 1.5 million homes per year over the past few years, but instead only about 500,000 homes were constructed. "We're going to have to catch back up in order to serve the needs of a growing population," he said. "We have to make up for the deficit we've had in the past years."

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The key force is a tight supply of housing exacerbated by a lack of land availability, he said. "What you're seeing with the builders is an inability to really get the land that we need to be able to build the homes to meet the demand," he said. "So you have inventories that are very, very low, and that is driving prices up."

Miller also said that the cost of commodities for builders is a "mixed bag" and that prices of homes are rising faster than costs. "I don't think you can read a lot from costs," he said, adding that although costs of raw materials are going down, other factors, like labor, are getting more expensive.

"We're starting to see a real recovery in housing that is not likely to be pulled back," he said.

(Read More: 'No Place Like Homebuilding')

— By CNBC's Paul Toscano. Follow him on Twitter and get the latest stories from "Squawk on the Street" @ToscanoPaul