Those nocturnal chats and other contacts between the man who now occupies the Oval Office and an infamous political trickster have come under intensifying scrutiny as special counsel Robert S. Mueller III’s investigation bores into whether Stone served as a bridge between Trump and WikiLeaks as the group was publishing hacked Democratic emails.

Mueller’s keen interest in their relationship was laid out in a draft court document revealed this week in which prosecutors drew a direct line between the two men — referring to Stone as someone understood to be in regular contact with senior Trump campaign officials, “including with then-candidate Donald J. Trump.”

The inclusion of the president by name in the draft filing rattled his legal team and indicated how closely the special counsel is scrutinizing what Trump may have learned from Stone about WikiLeaks’ release of emails that prosecutors say were hacked by Russian intelligence operatives.