Mr. Durham, the U.S. attorney in Connecticut assigned by Mr. Barr to review the Russia inquiry, has sought documents and interviews about how federal law enforcement officials handled an investigation around the same time into allegations of political corruption at the Clinton Foundation, according to people familiar with the matter.

Mr. Durham’s team members have suggested to others that they are comparing the two investigations as well as examining whether investigators in the Russia inquiry flouted laws or policies. It was not clear whether Mr. Durham’s investigators were similarly looking for violations in the Clinton Foundation investigation, nor whether the comparison would be included or play a major role in the outcome of Mr. Durham’s inquiry.

The approach is highly unusual, according to people briefed on the investigation. Though the suspected crimes themselves are not comparable — one involves a possible conspiracy between a presidential campaign and a foreign adversary to interfere in an election, and the other involves potential bribery and corruption — and largely included different teams of investigators and prosecutors, Mr. Durham’s efforts suggest the scope of his review is broader than previously known.