In a rare move for a stock market operator, BATS Global Markets Inc. is suggesting some stocks shouldn't trade on BATS exchanges.

Chris Concannon, newly appointed CEO and president of BATS, said the company was planning to file a new proposal to the Securities and Exchange Commission that would require thinly-traded stocks to trade only at the exchange where they are publicly listed.

That would mean more than 500 stocks would trade only on the exchanges operated by the New York Stock Exchange and Nasdaq OMX Group Inc., he said in an interview. There are roughly 8,000 stocks and exchange-traded funds traded on exchanges in the U.S.

Mr. Concannon announced the proposal in a letter to employees and market participants, saying the rule would "enable market participants to more efficiently form prices" in those stocks.

In an interview on Thursday afternoon, he said the idea was meant to help make the U.S. stock market simpler without trying to implement wide-ranging, potentially disruptive changes.

"We believe that small incremental changes are what the market can use today, not major market structure reform," he said.

The proposal comes as exchanges work out the details of a SEC-led pilot project to trade some illiquid stocks in five-cent increments, rather than one-cent increments. The number of stocks affected by the pilot project would be much larger than BATS's new proposal.

"We view the BATS Exclusive Listing Proposal as a potentially critical step toward de-fragmenting trading volumes of illiquid securities, for the benefit of all investors, and, particularly, for issuers of these low-volume stocks," Mr. Concannon wrote in the letter.

Critics of the U.S. stock market structure have long lamented its "fragmented" nature. A stock can be traded on any of 11 stock exchanges and more than 40 private trading venues, such as dark pools operated by large banks.

BATS would lose a minimal amount of revenue from the proposed change. The CEO said he hadn't sought out opinions on the proposal from NYSE President Tom Farley or Nasdaq CEO Robert Greifeld because he wanted the idea to be debated publicly. NYSE declined to comment and Nasdaq couldn't be reached immediately for comment.

The rule would only affect trading of those thinly traded stocks on exchanges. They could still be traded on private venues, Mr. Concannon added.

If the rule was passed, NYSE and Nasdaq could experiment with other changes to trading of those stocks to boost trading, such as having periodic auctions or wider tick sizes.

Write to Bradley Hope at bradley.hope@wsj.com

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