Schiff, Cummings and Engel, who chair the House Intelligence, Oversight and Foreign Affairs committees respectively, had requested the communications between Trump and the Russian president, citing a January report by The Washington Post.
Lowell would not tell the committee whether Kushner had ever used WhatsApp to discuss classified information.
He also confirmed that Ivanka Trump, President Donald Trump's daughter, continues to receive official emails on her personal email account and does not forward them to her official account, which is required by law, the letter noted. Cummings noted that in October 2017, White House lawyers briefed committee staff and "confessed" that several White House employees had failed to forward official records from their personal email accounts to their government accounts within 20 days, although they refused to identify the staffers.
That proposal is under investigation by Cummings' committee, which is looking into information from whistleblowers who have said they witnessed "abnormal acts" within the Trump National Security Council involving senior White House officials who were pushing the plan.
The White House did not respond to Newsweek's request for additional comment on the request from congressional committees.
"While we respectfully seek to accommodate appropriate oversight requests, we are unaware of any precedent supporting such sweeping requests", he wrote in a letter to Cummings, House Permanent Select Committee on Intelligence Chairman Adam Schiff, and Committee on Foreign Affairs Chairman Eliot Engel.
"In fact, as you know, the White House has not produced a single piece of paper to the committee in the 116th Congress - in this or any other investigation", Cummings wrote, referring to the current session of Congress, when Democrats took control of the House.
Lowell confirmed Kusher, President Donald Trump's, used the messaging service WhatsApp to communicate with world leaders. He acknowledged referring questions about Kushner's contacts through WhatsApp to the White House, and argued that Kushner "follows the protocols", including over classified information.
Lowell also said his discussion with the committee about Ivanka Trump's emails was specifically about the period before September 2017.
Other government officials, including Vice President Mike Pence (when he was governor of Indiana) have been found to have used private emails for government work. The White House has refused to turn over the documents.
The letter raises the latest concern about the use of private email and messaging applications to conduct official White House business. An attorney for McFarland declined to comment.
Cummings argues in his letter it could be a violation of the Presidential Records Act, which prohibits White House staff from using private email to conduct government business unless the individual forwards the message to the official account within 20 days. "The Committee requests that you confirm by March 28, 2019, whether you intend to comply voluntarily with its request or whether the committee should consider alternative means to obtain the information it needs to conduct its investigation", Cummings wrote.