“He sees more and more every single day that this is proving further and further to be a total witch hunt, particularly because it was based on a false and unverified and discredited dossier.”

— Sarah Huckabee Sanders, the White House press secretary, in a news conference on Monday

False.

Mr. Trump and Ms. Sanders repeated a false claim the president made in May, when he said the F.B.I. began investigating possible links between his presidential campaign and Russian election interference based on a dossier compiled by Christopher Steele, a former British spy.

The New York Times has reported — and Republicans who hold the majority vote on the House Intelligence Committee have concluded — that the investigation began in July 2016 and was prompted by the actions of George Papadopoulos, a foreign policy adviser to the Trump campaign.

Mr. Papadopoulos told an Australian diplomat in May 2016 that Russia had political “dirt” on Hillary Clinton, the Democratic presidential candidate. Australian officials then alerted their American counterparts of the conversation with Mr. Papadopoulos.

The information provided by Mr. Steele did not reach F.B.I. officials who were investigating Mr. Trump’s campaign until mid-September of 2016, The Times reported in May.