The president has recently taken to pointing to the volume of tests that have been administered — a misleading figure because, according to health experts, the more relevant figure is how many people are being tested per capita. In that regard, the United States still lags well behind other nations like South Korea.

Other governors also made it clear to Mr. Trump that they needed more supplies, if somewhat more delicately. Gov. Roy Cooper of North Carolina, a Democrat, told Mr. Trump: “As much as you can send us is very much appreciated.”

That prompted the president to note that “we have a lot of planes coming in” and that “Boeing gave us their big, monster cargo plane; it’s the biggest cargo plane in the world.”

At another point in the call, when someone asked if the governor of Utah was on the line, Mr. Trump cracked that he was probably visiting Mitt Romney, the state’s junior senator who has been in quarantine after coming into contact with Senator Rand Paul, Republican of Kentucky, who tested positive for the coronavirus.

A White House spokesman, Hogan Gidley, described the call this way: “The governors praised President Trump’s leadership, assistance and quick action to address this national crisis, and the president told the governors he would make sure that whatever they may need, he would direct his team to provide.”

And at the daily White House briefing on Monday afternoon, Mr. Trump described the call as an opportunity for the governors to thank his administration.

“I think for the most part, they were saying, Thank you for doing a great job,” he said.

Meanwhile, Mr. Inslee said on Monday that he was shocked to hear the president convey a lack of awareness about testing concerns and that he was hopeful the president would look into the issue.