WASHINGTON—Investigators are re-examining conversations detected by U.S. intelligence agencies in spring 2015 that captured Russian government officials discussing associates of Donald Trump, according to current and former U.S. officials, a move prompted by revelations that the president’s eldest son met with a Russian lawyer last year.

In some cases, the Russians in the overheard conversations talked about meetings held outside the U.S. involving Russian government officials and Trump business associates or advisers, these...