WASHINGTON — A Democratic senator asked the F.B.I. on Friday to open a perjury investigation into the homeland security secretary, Kirstjen Nielsen, over her congressional testimony about the Trump administration’s policy of separating migrant families at the southern border.

The senator, Jeff Merkley of Oregon, cited a previously unreleased document from December 2017 that showed that Ms. Nielsen’s staff considered a range of options for dealing with the influx of families seeking asylum, including a policy that would “separate family units.”

But testifying before the House Judiciary Committee last month, Ms. Nielsen said that “we’ve never had a policy for family separation.” She also denied in subsequent interviews and statements on social media that she had pursued such a policy.

“In light of these conflicting facts,” Mr. Merkley wrote in a letter to the F.B.I. director, Christopher A. Wray, “the F.B.I. should immediately investigate whether Secretary Nielsen’s statements” violate “federal statutes that prohibit perjury and false statements to Congress.”