“We have historically found ourselves occupying the last seat at the table when research is conducted on emerging public health issues that profoundly affect minority communities,” Dr. Hildreth wrote in a letter to the Meharry community. “We have paid a heavy price for being shut out.”

The debate highlights an ongoing, and heated, quandary in scientific research: Is it possible to take so much corporate money and not become biased in the funder’s favor?

Lindsay Andrews, a spokeswoman for Juul, said the company had no specific conditions for the grant, which will be paid over five years.

“There are many questions about the overall public health impact of vapor products, and Juul products in particular, that a robust body of public health research must help answer,” Ms. Andrews said.

Meharry, founded in Nashville in 1876, is the nation’s largest medical research center at a historically black institution. Dr. Hildreth, a Rhodes scholar with a Ph.D. from Oxford and an M.D. from Johns Hopkins, became president of the university in 2015 and is determined to expand its research. To do so, he has been in discussion with technology companies, foundations and the federal government, in addition to Juul.

Last summer, Dr. Hildreth and Patrick Johnson, Meharry’s senior vice president for institutional advancement, met with Juul representatives in Washington to ask the company to help underwrite a research program which would study, among other things, e-cigarettes.