The White House has instructed former White House staffers Hope Hicks and Annie Donaldson not to comply with the House Judiciary Committee's subpoenas to turn over documents related to their time in President Donald Trump's administration, House Democrats said Tuesday.

But former White House communications director Hope Hicks said she will still hand over documents related to Trump's 2016 presidential campaign, according to the House Judiciary Committee.

CNN first reported that Hicks and Donaldson would not fully comply with the House Democrats' subpoenas.

House Judiciary Committee Chairman Jerry Nadler, D-N.Y, said in statement that the White House's move was "part of President Trump's continued obstruction of Congress."

But Nadler noted that Hicks "has agreed to turn over some documents to the committee related to her time working for the Trump Campaign."

"I thank her for that show of good faith," Nadler said.

Politico, citing two sources familiar with Hicks' contacts with the Judiciary Committee, reported that the former White House staffer, who played a key role on the Trump campaign as communications director, has already begun providing documents to the panel.

Donaldson was former White House counsel Don McGahn's chief of staff. Her notes were heavily cited in special counsel Robert Mueller's report on Russian election interference, possible Trump-campaign coordination with the Kremlin and possible obstruction of justice by Trump.

The Judiciary Committee issued subpoenas for Hicks and Donaldson to testify before that panel and provide documents related to a sweeping probe of figures in President Donald Trump's orbit.

Both Hicks and Donaldson were ordered to produce the requested documents to the committee by June 4. Hicks' subpoena sets a June 19 date for her to testify in a hearing before the Judiciary Committee, while Donaldson is asked to appear June 24 for a deposition.

Hicks is now the executive vice president and chief communications officer for Fox Corporation.

"Federal law makes clear that the documents we requested — documents that left the White House months ago — are no longer covered by executive privilege, if they ever were," Nadler said in his statement.

"The President has no lawful basis for preventing these witnesses from complying with our request. We will continue to seek reasonable accommodation on these and all our discovery requests and intend to press these issues when we obtain the testimony of both Ms. Hicks and Ms. Donaldson," Nadler said.

It was unclear whether the committee would move to hold either Hicks or Donaldson in contempt of Congress.

The White House, Hicks and Donaldson did not immediately respond to CNBC's inquiries about CNN's report.

This is a developing story. Please check back for updates.