WASHINGTON — Republican senators are pressing the US government’s housing official to take steps to shore up the federal agency that insures mortgages for millions of borrowers. An audit shows the agency faces $16.3 billion in losses and might require a taxpayer bailout.

Shaun Donovan, secretary of housing and urban development, said Thursday at a hearing of the Senate Banking Committee that the agency, the Federal Housing Administration, has already taken action to strengthen its finances.