The special counsel’s office issued a rare statement late Friday disputing a BuzzFeed report that said President Trump directed his former lawyer, Michael Cohen, to lie to Congress about the president’s involvement in a real-estate deal with Russia during the 2016 campaign.

“BuzzFeed’s description of specific statements to the Special Counsel’s Office, and characterization of documents and testimony obtained by this office, regarding Michael Cohen’s Congressional testimony are not accurate,” said Peter Carr, spokesman for...