This move comes amid growing controversy over the SEC's emergency order that has been in place since Monday, and lasts for up to 30 days.
The emergency rule against so-called "naked short-selling" applies to only 19 financial entities, including the mortgage financiers Fannie Mae and Freddie Mac and big Wall Street banks.
A number of banks that were not included in the SEC's list have been lobbying the regulator to be included in the rule.
They argue that the SEC's decision to include only a limited number of institutions had made the rest of the financial sector more of a target for short-sellers.
People close to Washington Mutual, one of the largest US banks to be excluded, said the bank had become more vulnerable to short-sellers.
They said yesterday's 13 per cent fall in WaMu's shares, which was sparked by fears over its financial health, had been exacerbated by heavy short-selling.
Meanwhile, groups representing hedge funds, many of which are short-sellers, have been lobbying the SEC to not extend the rule to a broader list of stocks.