Under 2018 version of capital requirements, Fannie and Freddie would have been required to raise up to $180 billion

WASHINGTON— Fannie Mae FNMA -4.26% and Freddie Mac’s FMCC -3.27% federal regulator kicked off a process for the mortgage-finance companies to raise enough capital for them to return to private ownership.

The Tuesday announcement by the Federal Housing Finance Agency is a sign it thinks the companies likely need more than $180 billion in capital previously envisioned by the agency in 2018. At present, Fannie currently holds $6.4 billion in capital and Freddie holds $4.8 billion, according to the FHFA, far less than what they will need to eventually exit government control.

Tuesday’s move effectively restarts the process for setting heightened capital levels—cash to absorb possible losses—at the companies, with likely timing for a final rule in late 2020 or 2021.

Fannie and Freddie play critical roles maintaining the plumbing of the U.S. mortgage market. They purchase loans from lenders and repackage them as securities that are insured if the loans default, guaranteeing roughly half of the $10 trillion housing market.

The firms’ regulator seized the companies through a process known as conservatorship during the George W. Bush administration. The Treasury Department at the time agreed to inject vast sums to support some $5 trillion in debt securities issued by the companies.

Setting the companies’ capital requirement is just one of several hurdles to making the firms private. Another move came in September when the FHFA and the Treasury Department allowed Fannie and Freddie to retain as much as $45 billion of their earnings combined—ending a yearslong requirement the firms sweep most of their profits to U.S. Treasury.

FHFA Director Mark Calabria, in a written statement on Tuesday, said last year’s capital proposal by the FHFA—floated by an Obama-appointed predecessor—came before the companies began the process of retaining capital as a first step toward ending their conservatorships.

“In fairness to all interested parties, the comments submitted during the previous rule making were submitted under a different set of assumptions about the future of the enterprises,” he said. “During the process of the rule making, important issues were identified that will be addressed in the re-proposal.”

Write to Andrew Ackerman at andrew.ackerman@wsj.com