In Thursday's letter, Cummings said the White House's refusal to turn over documents is "obstructing the committee's investigation into allegations of violations of federal records laws" and potential breaches of national security.
The committee said that it learned about the use of private email and WhatsApp from a December 2018 conversation from Kushner's lawyer, Abbe Lowell, who also represents the president's daughter, Ivanka Trump.
Cummings also indicated that he was unsure whether or not Kushner had used WhatsApp to transmit classified government information.
The House oversight committee first launched their investigation into use of personal email "in violation of the Presidential Records Act and White House policy" back in 2017, Chairman Elijah Cummings, D-Md., wrote in Thursday's letter.
In the letter, Cummings noted that Kushner's lawyer had told Congress in December that Kushner used WhatsApp as part of his official duties but did not say whether such messages included classified information. He also said that the Oversight Committee learned that McFarland "conducted official business on her personal AOL.com account" when she was deputy national security adviser and that they had "also obtained a document that appears to show that Bannon, former White House Chief Strategist, received documents" related to transferring U.S. nuclear technology to Saudi Arabia.
Section 2209 of the statue stipulates White House officials are required to forward a "complete copy" of "official business conducted using non-official electronic messaging accounts" to "an official electronic messaging account of the President, Vice President, or covered employee" no later than 20 days after the creation of the communication.
The requirement for her to preserve her communications was outlined in a law which is similar to the one which governs the preservation of White House records.
According to Democrats' letter, Lowell confirmed to lawmakers Kushner's use of the app, but that Lowell also claimed that Kushner has been complying with the law by screenshotting the messages and sending them to his White House email account or to the National Security Council.
Additionally, it was revealed late a year ago that the president's daughter and senior adviser Ivanka Trump used a private email account to send hundreds of emails to Cabinet officials, White House aides and personal assistants throughout much of 2017.
In his letter to Cipollone, Cummings demanded that the White House produce documents related to their investigation into this matter by April 4.
He also said he referred Cummings to the White House counsel's office for questions about Kushner's use of the application.
Lowell didn't immediately respond to a request for comment.
Lowell's response Thursday said that he was discussing specifically a period before September 2017. Rather, she forwards on the government-business-related emails she replies to, according to the Democrat's account of Lowell's explanation.
Robert Giuffra, a lawyer for McFarland, declined comment.
He said the document was related to efforts by McFarland and other White House officials to transfer sensitive US nuclear technology to Saudi Arabia "in coordination with Tom Barrack, a personal friend of President Trump and the chairman of President Trump's inaugural committee".
Cummings says that he expects to hear back from the White House or will be forced to pursue other avenues to obtain the information he has requested.
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