Nasdaq shares fell more than 2 percent in late trading Tuesday after the announcement of a secondary offering of shares that will allow Borse Dubai to reduce its minority stake in the U.S. exchange.

Borse Dubai, which was the largest single shareholder in Nasdaq, said it would cut its ownership stake from 15.5 percent to 10.8 percent.

The Dubai Stock Exchange will sell about 26.96 million Nasdaq shares as part of a secondary offering, according to a statement issued after the close on Tuesday.

Nasdaq shares ended the regular session up 3.6 percent at $62.46.

In a separate statement, Nasdaq set the price of the Dubai Stock Exchange's offering at $59 per share.

The Dubai Stock Exchange will receive about $1.6 billion from the sale of shares.

After the offering, Borse Dubai will become the second largest shareholder in Nasdaq.

US private equity firm Thoma Bravo will become Nasdaq's largest shareholder with a 12.5 percent stake in the US stock exchange, or about 71.6 million shares.