Jared Kushnerused WhatsApp to communicate with foreign leaders, Democrats have claimed.
Using the encrypted messaging service for government duties could violate a law banning White House officials from employing non-official electronic messaging accounts.
Elijah Cummings, Democrat chairman of the House oversight committee, asked the White House to provide information on whether Mr Kushner, a senior adviser to the president, had used WhatsApp to communicate sensitive or classified details.
Mr Cummings suggestions were based on comments made to the committee by Abbe Lowell, Mr Kushner's lawyer.
However, Mr Lowell later said the committee chairman's characterisation of what he said was "not completely accurate".
Mr Lowell denied saying that Mr Kushner had been communicating with foreign "leaders" or "officials".
He said Mr Kushner had many friends abroad and that he only used the messaging service to talk to "some people".
Mr Cummings also suggested that Ivanka Trump - the president's daughter and Mr Kushner's wife - had continued to use a personal email account while a White House adviser, which would violate the Presidential Records Act.
But Mr Lowell denied having told the committee that the president's daughter was doing that.
He indicated that she "always forwards official business to her White House account".
Donald Trump said he knew nothing about Mr Kushner's use of WhatsApp.
He said: "I know nothing about it. I've never heard that, I've never heard about it."
In the 2016 presidential campaign Mr Trump railed against Hillary Clinton, his Democrat opponent, over her use of a private email server while she was serving as secretary of state.
Mr Kushner's communications, particularly with foreign leaders, have been under scrutiny and officials have previously raised questions over whether he should be given a top-secret security clearance.