President Donald Trump insisted again Tuesday that the U.S. would have fewer coronavirus cases if it conducted less testing — even as outbreaks continue to surge across the nation and deaths begin to pick up pace. 

“Think of this, if we didn’t do testing, instead of testing over 40 million people, if we did half the testing we would have half the cases,” Trump said at a press conference at the White House. “If we did another, you cut that in half, we would have, yet again, half of that. But the headlines are always testing.” 

Trump said that while coronavirus testing “is a good thing,” it has also served as “fodder for the fake news to report cases.” He said that if the U.S. didn’t test people for Covid-19, then you wouldn’t have “all the headlines” because the nation has one of the lowest mortality rate. 

“When I turn on the news I see cases, cases, cases,” Trump said. 

The U.S. has more coronavirus cases than any other country in the world with more than 3.4 million out of the roughly 13.3 million global cases. While the U.S. has conducted more testing than any other country, it also has the most fatalities — 136,300 of the world’s approximately 576,800 deaths. Covid-19 deaths, which had been on the decline in America for almost two months, recently began rising again, according to data compiled by Johns Hopkins University. 

Average daily deaths in the U.S. peaked in mid-April at more than 2,400, based on a seven-day moving average. Fatalities had been on the decline since then, bottoming out at an average of just over 500 a day on the Fourth of July, but they’ve been rising ever since to an average of 700 Covid-19 deaths on Monday, according to Hopkins data. 

Across the country, more than a third of U.S. states reported record highs in daily new cases, based on a seven-day moving average as of Monday, according to a CNBC analysis of data compiled by Hopkins. Twenty states, including Florida and Georgia, broke records on Monday with an average of 10,855 and 3,358 new cases, respectively. 

As cases continue to surge, labs across the nation are falling behind in processing and delivering test results, according two of the country’s biggest lab diagnostics companies. 

“We attribute this demand primarily to the rapid, continuing spread of COVID-19 infections across the nation but particularly in the South, Southwest and West regions of the country,” Quest Diagnostics said in a statement.

Hospitalizations across the country, which epidemiologists say could show the most severe outbreaks since they don’t rely on testing, continue to hit new record highs indicating widespread community transmission. On Monday, 14 states broke grim records in seven-day average hospitalization numbers, including Texas, California and Arizona, according to a CNBC analysis of data from the Covid Tracking Project. 

— CNBC’s Nate Rattner, Jasmine Kim and Will Feuer contributed to this report.