WASHINGTON—The House Oversight and Reform Committee failed to reach an agreement with Attorney General William Barr and Commerce Secretary Wilbur Ross and will move forward with a contempt vote next week for ignoring its subpoena seeking information about efforts to add a citizenship question to the 2020 census.

Oversight Committee Chairman Elijah Cummings (D., Md.) said this week that Messrs. Barr and Ross had until Thursday to comply with subpoenas sent two months ago. The departments say the documents that Democrats are...