By Clare Foran and Lauren Fox, CNN

(CNN) -- The Department of Justice informed the House Oversight Committee on Wednesday that President Donald Trump has asserted executive privilege over materials related to the addition of a citizenship question to the 2020 census.

The move comes ahead of a vote in the committee about whether to hold Attorney General William Barr and Commerce Secretary Wilbur Ross in contempt of Congress over a dispute related to the census and for not complying with subpoenas issued by the committee.

In a letter to Committee Chair Elijah 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."

Cummings told the committee on Wednesday that he would postpone the contempt vote until later in the afternoon so lawmakers could review the letter.

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 the committee is voting on and what's next

The Democratic-led committee will be considering a census 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 itself includes citations for both civil and criminal contempt.

It's unclear what will happen after the committee votes on the resolution, but the vote will mark the latest escalation in hostilities between House Democrats and the Trump administration as Democrats press ahead with wide-ranging oversight investigations into the President and the executive branch.

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

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 has called the planned committee vote "an empty stunt," and 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.