The announcement was another reversal for the president and underscored the recurring dysfunction in the White House selection and vetting process that has plagued the administration. Mr. Ratcliffe joined a long list of Trump administration appointees who have had to pull their names after the president announced his plans to put them in powerful posts without a full picture of potentially disqualifying details.

Mr. Trump promised to announce a new nominee soon. Pete Hoekstra, the American ambassador to the Netherlands and a former chairman of the House Intelligence Committee, is one of the leading candidates for the post, according to two people briefed on the discussions. He wants the position, they said, and his long service on Capitol Hill and work helping create the job of director of national intelligence could make him more palatable to senators.

As soon as Mr. Ratcliffe was named, his qualifications came under scorching examination, including that he had embellished his credentials as a former federal prosecutor in East Texas, portraying himself as having deep experience putting terrorists in prison and shaping the George W. Bush administration’s counterterrorism policy.

In fact, while he was given the responsibility of coordinating any terrorism matters that arose for his office — a role every district was required to assign to someone — there were no significant national security prosecutions in that jurisdiction during his tenure, according to former colleagues.

Mr. Ratcliffe, who also briefly served as an interim United States attorney, also exaggerated his role in a major crackdown on the employment of undocumented immigrants by a poultry producer, taking all the personal credit for what was actually a multistate, multiagency operation.