Two top stock exchanges laid out their vision on Tuesday for how they believe U.S. regulators could craft rules to foster the creation of "venture exchanges" that list small-cap companies.

In prepared testimony before a U.S. Senate Banking panel, executives from Intercontinental Exchange's New York Stock Exchange and Nasdaq OMX discussed some of their most detailed suggestions to date on the subject.

Tuesday's hearing came just a few weeks after Securities and Exchange Commission Chair Mary Jo White announced in a speech that the agency is actively pursuing ways to promote venture exchanges.

The SEC review is part of a broader effort to help smaller companies thrive.

SEC Trading and Markets Division Director Steve Luparello, who also appeared before the panel, did not elaborate on what the SEC may do.

But he told lawmakers that the SEC is debating whether it should petition Congress for authority to exempt venture exchanges from federal "unlisted trading privileges" rules which permit stocks to be traded on rival exchanges where they are not listed.

"There is a certainly a way you can read the statute that is very restrictive," Luparello told lawmakers.

Executives from the NYSE and Nasdaq pitched different approaches on how to foster listings of smaller stocks.

NYSE President Thomas Farley laid out in his testimony a proposal for a new regime he said could work for stand-alone venture exchanges for companies with a public float of about $1 million.

Such exchanges, he said, should have similar self-regulatory functions in place to ensure compliance with market rules. But he said such exchanges should be exempted from the unlisted trading privileges rules to bolster liquidity.