Issa was just one of the lawmakers to express concerns about the IPO for Facebook, which has seen its stock price plummet to under $20 a share.
For his part, Issa has written to Schapiro twice in recent months, saying that Facebook has raised broader questions about the IPO process.
The California Republican has said that regulations overseeing the process need to be modernized, with investment banks having gotten an upper hand through a 1933 securities act that he says is loaded with conflicts of interest.
In her letter to Issa, Schapiro acknowledged that the commission was reviewing current rules in large part because of technological advancements since 2005, the last time the SEC completed a major reform.
But the chairwoman also defended those 2005 changes, saying they allowed investors of all stripes to gain more information before an IPO.
Schapiro also noted that some people believe there is too much focus on institutional investors in initial offerings. She also noted that others believe professional investors' involvement can add more certainty to the IPO process and a stock’s pricing.
The Wall Street Journal first reported Schapiro's letter to Issa.