Nevada, meanwhile, reported Saturday that there were almost 1,100 new confirmed cases in one day, a total that is almost double the state's previous single-day record.
"We got into June and COVID kind of fell off the headlines", Governor Ron DeSantis told reporters.
Texas and Florida closed bars and reimposed other curbs on Friday as the number of infections in the USA hit a single-day record with increases in 16 states, mostly in the south and west.
"Right now we are penalising those who don't wear masks", Mr Suarez said, adding that he was looking at potentially implementing new measures: "We may have to, at some point, implement a stay at home order".
The U.S. experienced its largest single-day increase in new COVID-19 cases on Thursday according to figures from Johns Hopkins University.
As situations spike, USA tourists are "not likely" to be permitted into the European Union as the bloc commences opening up to intercontinental travel, numerous EU diplomats told CNN.
The 36 states viewing a rise in cases contain: Alabama, Alaska, Arizona, Arkansas, California, Colorado, Florida, Georgia, Hawaii, Idaho, Illinois, Iowa, Kansas, Kentucky, Louisiana, Maine, Michigan, Minnesota, Mississippi, Missouri, Montana, Nevada, New Mexico, North Carolina, Ohio, Oklahoma, Pennsylvania, South Carolina, Tennessee, Texas, Utah, Vermont, Washington State, West Virginia, Wisconsin and Wyoming.
Despite the grim news from Texas, Florida and elsewhere, President Donald Trump said on Friday the United States was coming back from the crisis, which has halted large parts of the economy and left millions jobless. The variety rivals that of New York's peak in everyday cases in early April.
Florida's governor said there was no plan to continue reopening step-by-step.
"Phase 4 would mean a return to normal activity and we can't do that now", the statement said. "This is an evolving problem and we will proceed to make conclusions primarily based on the knowledge".
The new record for positive COVID-19 tests recorded by Reuters comes as several states at the center of a new surge in infections took steps back from efforts to ease restrictions on businesses.
Washington State Gov. Jay Inslee introduced Saturday he is hitting the pause button on the state's reopening approach owing to climbing instances.
A day later, Abbott also said he was closing bars and limiting restaurant capacity.
Spiking numbers there and in several other USA states marked a dramatic setback to efforts to reopen and salvage badly battered economies - efforts pushed by President Donald Trump.
In recent days, officials across the United States have reported a rise in cases among younger groups.
"There is a sense that a lot of young people, well you're young so you feel a little bit more invincible but, respectfully, often that can be a selfish mindset", Newsom said. In Mississippi, officials pointed to fraternity parties as one of the drivers behind the state's cases.
In Florida, the average age of people infected has dropped sharply - to 33 from 65 two months ago. The state's neighborhood transmission, he mentioned, is "becoming driven by that 18 to 35-12 months-old team".
"You have a responsibility to be careful if you're in contact with somebody who is more vulnerable", he said.
But now, some places that appeared to have avoided the worst are seeing surges of infections, as worries shift from major cities to rural areas.