With worries over Greece's status in the euro zone leaving some investors wary about the state of the euro, bitcoin wallet company Coinbase is offering to waive fees for customers using the European currency to buy or sell the cryptocurrency.

Coinbase's founder and CEO, Brian Armstrong, told CNBC's "Squawk Alley" that he's seen a fourfold increase in people buying bitcoin across the euro zone in just the last 48 hours.

"The situation in Greece has sparked an interest across the euro zone," Armstrong said, noting that "the numbers out of Greece are relatively small."

"In some ways it's very difficult to get bitcoin there now," he said. "The banks there are already closed."

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