The Justice Department on Monday told the chairman of the House Intelligence Committee that it had complied with his requests to the extent legally permissible, pushing back against his Monday evening deadline for more documents related to the FBI’s investigation of President Donald Trump’s 2016 campaign.

In a letter to Rep. Devin Nunes, a California Republican, Assistant Attorney General Stephen Boyd wrote that the department’s efforts to accommodate the committee’s demands while protecting ongoing investigations were “consistent...