President Donald Trump on Tuesday unexpectedly fired FBI Director James Comey, plunging the capital into confusion and immediately intensifying calls for a special prosecutor to assume control of the highly sensitive investigation into possible ties between the Trump campaign and Russia.

The reason for the firing, according to White House and Justice Department officials, was Mr. Comey’s much-criticized handling of an investigation into Hillary Clinton’s use of a private email server while secretary of state. The White House...