President Donald Trump’s pick to lead Fannie Mae and Freddie Mac’s regulator pledged to work with Congress on overhauling the companies, while downplaying controversial positions he’s previously laid out on everything from the 30-year-mortgage to affordable housing initiatives.

Mark Calabria, the libertarian economist who Trump has nominated to lead the Federal Housing Finance Agency, told senators Feb. 14 that they should play a leading role in pursuing changes for the mortgage giants, which have been under U.S. control since 2008. He outlined what he thinks should be the goals of any reform effort, emphasizing the need to dial back Fannie...