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If the rise in cases was solely attributable to more testing, the rate of positive test results would decrease or at least hold steady. But while the number of daily tests performed has steadily increased from under 100,000 in March to 460,000 to 640,000 this week, the positive rate had fallen from 10 to 20 percent in early March to about 4 percent in early June before climbing back up to 5 to 7 percent this week.

Increased testing in other countries has not produced the uptick in the positivity rate seen in the United States. Russia, for example, has ramped up its testing to about 300,000 a day in recent weeks from about 200,000 in May. But its positive rate has continued to hover at around 3 to 5 percent.

In states with the most severe outbreaks, that trend is starker still. Positive rates in Texas and Florida have increased to 10 to 20 percent this week from rates that were generally below 10 percent in May — a reality the Republican governors of both states have acknowledged.

“Clearly you’re seeing this, this is real,” Gov. Rick DeSantis of Florida said during a news conference on Tuesday. “Now they are testing more than they were for sure, but they’re also testing positive at a higher rate than they were before. And so that would tell you there’s probably been an escalation and transmission over the last seven to 10 days.”

Gov. Greg Abbott of Texas acknowledged the same point.

“If you look at the growth or even the decline in the number of people who were testing positive as well as the positivity rate all the way through the early part of May, Texas was moving in a very productive position,” he said on Monday. “Then around the time of Memorial Day, there was an increase, and that increase has maintained for several weeks now, necessitating that next steps be taken.”

What Was Said

“Fatalities are declining all across the country.”

This is misleading. While official death counts are most likely underreported, Mr. Pence is right that nationwide, deaths are continuing to decrease, though fatalities are rising or holding steady in several states such as Arizona, California, Florida, North Carolina and Texas.

Moreover, public health experts have urged caution that this will continue to be the case. Asked whether still declining fatalities were because of younger, healthier people contracting the disease, Dr. Anthony S. Fauci, the nation’s top infectious disease expert, told Congress this week that it was “too early to make that kind of link.”

“Deaths always lag considerably behind cases,” he said. “You might remember that at the time that New York was in their worst situation where the deaths were going up and yet the cases were starting to go down, the deaths only came down multiple weeks later.”

Curious about the accuracy of a claim? Email factcheck@nytimes.com.