The Office of Federal Housing Enterprise Oversight reduced the requirement from 30 percent to 20 percent, having imposed the restriction after accounting errors and a lack of risk-management controls were discovered several years ago, The Wall Street Journal reported.

The change could add $200 billion in relief for the mortgage securities market, the report said.

U.S. Treasury Secretary Henry Paulson said he was "encouraged" by the development.

"Additional capital will enable the companies to help more homeowners and will strengthen the underlying fundamentals of the mortgage market," Paulson said in a statement.

The requirements were reduced as Fannie Mae has complied with all the reform changes regulators asked. Freddie Mac is one step short of completing its list of changes.

Regulation director James Lockhart said he would lift the consent order on the two firms, but said each promised to maintain "prudent cushions" above the new capital requirements.