WASHINGTON — The head of a housing trade group criticized attempts to pare down the mortgage portfolios held by Fannie Mae (FNM) and Freddie Mac (FRE), saying they would have “a domino effect on the housing finance system as a whole.”

Jerry Howard, chief executive officer of the National Association of Home Builders, said at a press conference Wednesday that reining in the government-sponsored enterprises would make housing less affordable.

Mr. Howard’s trade group has been an ally of Fannie Mae and Freddie Mac as Senate Republicans have called for curbs on the combined $1.4 trillion portfolios held by the companies, which buy mortgages on the secondary market, among other things.

“If you do what some on the Hill are suggesting, in terms of reining in Fannie Mae and Freddie Mac’s abilities to hold their own portfolios…then you will create a diminishment in either the availability of capital to the housing finance system or the cost of capital,” Mr. Howard said. “And that will have an impact on housing affordability. There’s no question about that.”

Senate Banking Committee Chairman Richard Shelby, R-Alabama, is pushing a bill that would create strict new limits on the types of assets Fannie Mae and Freddie Mac could hold in their portfolios. Mr. Shelby, and others, have alleged that the portfolios are too large and pose a risk to the financial markets if either of the companies stumbled. Both are emerging from multibillion-dollar accounting scandals.

Most Senate Democrats have opposed the Senate bill, and Mr. Shelby has not been able to bring it to the floor for a vote. The House passed a bill last year that would give a new GSE regulator more discretion over the portfolios without directing the regulator to strip out certain assets.

Fannie Mae has estimated that Mr. Shelby’s bill would cause its portfolio to shrink to between $10 billion and $100 billion from $730 billion.

GSE critics have questioned, though, how much of a benefit Fannie Mae and Freddie Mac add to housing affordability. Several studies by Federal Reserve economists have argued that the housing GSEs only impact mortgage interest rates by a few basis points, not the 20 to 25 basis points that others have claimed.

Separately, Mr. Howard and NAACP president and chief executive officer Bruce S. Gordon released a report Wednesday calling for public policy changes that would increase the percentage of minority homeowners.

Among other things, the report called for the elimination of abusive lending practices and the better enforcement of Fair Housing Act laws.