WASHINGTON--Market executives called for an overhaul of stock market trading rules in a Senate hearing Tuesday, saying the shift to high-frequency and off-exchange trading has created too much complexity that favors the most sophisticated investors.

The hearing, the second by the Senate Banking Committee on computer-driven trading in the past month, comes amid heightened scrutiny of off-exchange venues such as dark pools and high-frequency trading, which accounts for about half of all trading in U.S. stocks.

Jeffrey Sprecher, chief executive of IntercontinentalExchange Inc., which owns the New York Stock Exchange, said at the hearing that regulations have led to an overly fragmented and complex market in which too much trading takes place away from stock exchanges. Such complexity "hurts market confidence and I believe deters some investors and entrepreneurs from accessing the public markets," Mr. Sprecher said.

Kevin Cronin, global head of trading at asset manager Invesco Ltd., with $790 billion under management, said regulations have encouraged market fragmentation, which can favor sophisticated traders.

"Markets have become too complex and fragmented not because they need to be but rather because we have allowed them to become so," he said, adding that complex rules governing dark pools "have facilitated an unlevel playing field that unfairly favors sophisticated participants over ordinary investors."

Two weeks ago, New York Attorney General Eric Schneiderman alleged in a complaint that Barclays PLC lied about how it favors high-frequency traders in its dark pool. Securities and Exchange Commission Chairman Mary Jo White in a speech in New York last month vowed to ratchet up oversight of computer-driven trading and dark pools, which don't post traders' buy and sell orders, only reporting trades after they are executed.

Stock trading in the U.S. has seen an increase in "complexity and instability in the system," said Sen. Tim Johnson (D, S.D.), chairman of the committee, said at the hearing. While trading has evolved dramatically in recent decades, "many rules and market conventions date back to the days of less complex markets."

Kenneth Griffin, chief executive of Chicago hedge fund Citadel LLC, said dark pools can favor some trading firms over others, giving them unfair advantages. Some dark pools "may refuse access to certain market participants...and charge different fees to different types of participants," he said. Many dark pools also "offer economic inducements to broker-dealers and high-frequency traders to route their orders to them," Mr. Griffin said.

Mr. Sprecher, reiterating a concern he has voiced several times since ICE purchased the New York Stock Exchange last year, called for the elimination of a fee and rebate system known as "maker taker." He said the system adds to "the complexity and the appearance of conflicts of interest." Mr. Sprecher also said regulators should favor public exchanges, which he said add to price discovery for stocks, over more opaque off-exchange venues such as dark pools.

Sen. Elizabeth Warren (D., Mass.) questioned the market benefit of high-frequency trading, since many high-speed firms only hold a stock for a few seconds or minutes before selling it to another firm. "I'm trying to figure out how that adds more liquidity to the market if that seller would have found that buyer" without the high-speed firm jumping in the middle of the transaction, she said.

"We are worried about excessive intermediation in the markets," Mr. Cronin said in response to her questions.

Write to Scott Patterson at scott.patterson@wsj.com

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