Billionaire hedge fund pioneer Leon Cooperman told CNBC on Thursday that the stock market is not overvalued yet.

The chairman and CEO of Omega Advisors characterized it as "reasonably fully valued."

"The market is doing better this year than I thought," he said. "[But] I don't see euphoria."

Cooperman appeared on "Fast Money Halftime Report" as the Dow Jones industrial average and the were trading less than 1 percent away from their closing record highs.

He said he looks at the equity market one stock at a time, adding his biggest holding is Google-parent Alphabet. He does not think Amazon is a monopoly.

He also said the economy is gaining momentum.

Cooperman, who he has met in the Oval Office with President Donald Trump, thinks the Republican tax overhaul bill makes sense. Taxes going down for businesses is a positive, he said.

If Hillary Clinton had won the presidential election, the United States would be in a recession, said Cooperman, who added he's a registered independent.

The nation is better off with Trump as president than it would have been under Clinton or the other major 2016 Democratic contender, Sen. Bernie Sanders.

There was also lots of attention on bitcoin, which blasted through the $19,000 level on the Coinbase platform on Thursday before pulling back in a two-day wild ride.

Asked his opinion on bitcoin, Cooperman said, "I dont know anything about it," adding he has no money in it.

He did say blockchain, the technology underlying the digital currency, is "interesting."

But bitcoin going from $1,000 earlier this year to $19,000 does not make sense, Cooperman said. "There is euphoria in bitcoin," he said, but stressed again there's no euphoria in the stock market.

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