Smith has sat down to answer lawmakers’ questions about the cases involving Mr. Trump twice before. In December, he testified for more than eight hours during a closed-door deposition before the House Judiciary Committee.

During that deposition, Smith was asked about subpoenas his team issued for toll records for certain members of Congress. He told the committee that he did not seek a search warrant for the content of text messages from lawmakers, only the toll records.

But Republicans have accused Smith of lying during his appearance because of information revealed by the Senate Judiciary Committee in July.

The Justice Department provided documents to the Senate committee that showed Smith’s team had sought and obtained text messages from the National Archives and Records Administration, which included messages from 44 members of Congress — Republicans and Democrats.

Smith addressed his decision to analyze Republicans’ phone records in January, when he appeared before the panel in a public setting.

“The conspiracy that we were investigating, it was relevant to get toll records to understand the scope of that conspiracy, who they were seeking to coerce, who they were seeking, to influence who was seeking to help them,” Smith said.

He said securing the phone records, which only contained data about the calls and not their contents, is “common practice” in complex investigations.

During that hearing, Smith also defended his handling of the investigations involving Mr. Trump and told House members he pursued the unprecedented charges against the president “because the evidence established that he willfully broke the law — the very laws he took an oath to uphold.”