Washington (CNN) The House Oversight Committee voted on Wednesday to hold Attorney General William Barr and Commerce Secretary Wilbur Ross in contempt of Congress over a dispute related to the addition of a citizenship question to the 2020 census. The vote was 24-15.

The vote came just hours after President Donald Trump asserted executive privilege over materials related to the citizenship question, a move that further escalated tensions between House Democrats investigating the 2020 census and the administration.

The Democratic-led committee voted on a contempt resolution that recommends that the House of Representatives find Barr and Ross in contempt of Congress "for refusal to comply with subpoenas." The contempt resolution includes citations for both civil and criminal contempt.

Republican Rep. Justin Amash of Michigan joined with Democrats on the committee to vote in favor of the resolution.

Ross called the move an "empty stunt" in a statement and said, "Today, the Democrats maintained their shameless, weekly attacks on this Administration without consideration for the truth."

The Commerce Secretary said that the committee "isn't interested in cooperation" and "demonstrated its scorn for the Constitution" by holding the vote.

"This is a disappointing day for Congress and our country. America deserves better," Ross said.

The Justice Department fired back at the contempt finding, accusing the committee of playing "political games" and saying the panel's "attempt to define the Department of Justice's good-faith cooperation as 'contempt' defies logic."

Justice Department spokesperson Kerri Kupec went on to say that DOJ had worked "tirelessly" to respond to the committee's requests.

"Today's action by Chairman Cummings and his Committee undermines Congress's credibility with the American people," Kupec said.

Rep. Jim Jordan, the top Republican on the committee, called the vote "unwarranted" in a statement as well as "a misuse of the committee's contempt authority."

"This vote was another act of political theater designed to interfere with the Supreme Court's consideration of the reinstitution of a citizenship question on the 2020 Census," Jordan said.

House Oversight Chairman Elijah Cummings said in a statement that the "contempt vote was the last thing I wanted to do," adding, "I bent over backwards to try to work with the Administration, but they delayed, dissembled, and degraded our Committee's efforts to conduct this investigation and fulfill our responsibilities under the Constitution."

It's unclear what will happen now that the committee has voted on the resolution. Depending on how the Departments of Justice or Commerce respond, House Democrats could go to the floor with both criminal and civil contempt. They could also drop criminal before going to the floor if some accommodation happens.

According to a committee aide, a criminal contempt vote would have to go through the floor. However, civil contempt could go through the Bipartisan Legal Advisory Group, which is made up of the three highest-ranked House Democrats and two highest-ranked House Republicans.

Earlier Wednesday, the Department of Justice informed the House Oversight Committee that Trump has asserted executive privilege over materials related to the addition of a citizenship question to the 2020 census.

In a letter to Cummings, Assistant Attorney General Stephen Boyd wrote , "this letter is to advise you that the President has asserted executive privilege over certain subpoenaed documents identified by the Committee in its June 3, 2019 letters to the Attorney General and the Secretary."

Cummings, a Maryland Democrat, has said that he scheduled the vote because the attorney general and commerce secretary have not complied with subpoenas issued by the committee as it investigates the Trump administration's push to add the question to the census.

Cummings criticized the assertion of executive privilege Wednesday morning.

"This does not appear to be an effort to engage in good-faith negotiations or accommodations," he said. "Instead, it appears to be another example of the administration's blanket defiance of Congress' constitutionally-mandated responsibilities."

The specific documents at the heart of the fight -- mainly a set of drafts memos and letters exchanged between Commerce and Justice -- are covered by certain privileges, according to the Justice Department.

At least one federal court in a different, but related case, agreed with the administration and concluded that the documents were appropriately withheld -- a fact that may bolster DOJ's case if House Democrats take the document production issue to court.

The Commerce Department announced last year that a citizenship question would be included in the upcoming 2020 census. The move has sparked controversy and a high-stakes court battle as critics say that asking about citizenship status will lead to an inaccurate count.

Census data serves as the basis for decisions about how to allocate federal resources and draw congressional districts.

President Donald Trump defended the addition of a citizenship question on Wednesday, saying in remarks to reporters from the Oval Office, "it's totally ridiculous that we would have a census without asking."

What happens next

Cummings told CNN on Tuesday that he's not sure what the next step after his committee would be and if he'd push for a full House vote.

"We will decide that when the time comes," Cummings said of next steps.

"If they come to us, we will certainly talk to them, but I don't anticipate that," Cummings added, referring to the possibility of a deal or any accommodation being reached ahead of the vote.

The Justice Department and Commerce Department have both argued that they are working in good faith to respond to the requests from the committee and have already submitted thousands of pages of documents to the panel.

Ross said in an interview with CNBC on Tuesday said, "Please don't tell me we're not cooperating."

"What we are doing is cooperating in a rational way that's consistent with the rules, the regulations, the laws and prior practice," Ross said, adding, "We have produced to the House Oversight Committee 14,000 pages of material. I testified before them for almost seven hours. We're producing three more witnesses."

A Democratic committee aide told CNN, however, that those documents have been insufficient and are either publicly available documents, heavily redacted or just not responsive to the request at all and unrelated.

This story has been updated with additional developments Wednesday.