The U.S. Justice Department has begun this year to more sternly address perceived shortcomings in disclosures of consultants’ influence work for foreign countries, demanding more information as part of a wider scrutiny of secret lobbying for overseas interests.

In recent months, the Justice Department has sent what amounts to cease-and-desist orders requiring consultants to correct deficiencies in past disclosures or stop working for the overseas client that gave rise to a registration as a so-called “foreign agent,” a Justice Department official said.