The Education Department opened investigations into Harvard and Yale as part of a continuing review that it says has found U.S. universities failed to report at least $6.5 billion in foreign funding from countries such as China and Saudi Arabia, according to department materials reviewed by The Wall Street Journal.

The investigations into the Ivy League schools are the latest in a clash between U.S. universities and a coalition of federal officials including law enforcement, research funders such as the National Institutes...