WASHINGTON — President Obama will seek hundreds of millions of dollars for a new initiative to develop medical treatments tailored to genetic and other characteristics of individual patients, administration officials say.

The proposal, mentioned briefly in his State of the Union address, will be described in greater detail in his budget in the coming weeks. The effort is likely to receive support from members of both parties, lawmakers said.

“This is an incredible area of promise,” said Senator Bill Cassidy, Republican of Louisiana and a gastroenterologist. “There will be bipartisan support.”

Mr. Obama called it precision medicine, but the terms “personalized medicine” and “individualized medicine” are also widely used to describe the evolving field in which, for example, a doctor prescribes a medication that targets a specific mutation in a patient’s genes.