WASHINGTON — President Trump told a group of governors on Monday morning that they should not wait for the federal government to fill the growing demand for respirators needed to treat people with coronavirus.

“Respirators, ventilators, all of the equipment — try getting it yourselves,” Mr. Trump told the governors during the conference call, a recording of which was shared with The New York Times. “We will be backing you, but try getting it yourselves. Point of sales, much better, much more direct if you can get it yourself.”

The suggestion surprised some of the governors, who have been scrambling to contain the outbreak and are increasingly looking to the federal government for help with equipment, personnel and financial aid. Last Wednesday, Mr. Trump directed his labor secretary to increase the availability of respirators, and he has generally played down fears of shortages.