Infections are also up in some other parts of the world that have reopened, including the Czech Republic, which recently marked its biggest spike in virus cases in months.
Nearly 125,000 Americans have died of COVID-19, the highest known death toll from the highly infectious disease in the world.
Brazil - the second hardest-hit country after the USA - recorded 990 deaths on Saturday, the highest toll in the world that day, while Mexico recorded the second highest at 719.
"We have to be very careful", he said.
"But in the case of negligence and significant spread of the disease, economic problems will increase, too", he said.
Meanwhile stars including Coldplay, Miley Cyrus and Jennifer Hudson lent support to a European Commission-led drive Saturday that raised 6.15 billion euros ($6.9 billion) to support vaccine research and help make it available to poorer countries.
Some of those countries are still far from reaching their peak in infections, authorities say. The bulk of the local cases were detected in the densely populated Seoul metropolitan area, linked to nightclubs, church services, a huge e-commerce warehouse and low-income workers.
During a White House Coronavirus Task Force briefing on Friday, the first full briefing in almost 2 months, Pence noted that 34 states are experiencing a "measure of stability" - New York, New Jersey, and CT in particular - while 16 have rising new daily cases and a rising percentage of positive cases. Some experts have expressed doubt that deaths will return to that level because of advances in treatment and because many infections are happening in younger adults, who are more likely than older ones to survive. Some counties have been preparing to enter the fourth phase of reopening, "which would fundamentally necessarily mean no limitations", the governor's place of work explained in a statement. Some Florida cities canceled July 4 fireworks displays. In all, more than 663,500 recoveries have been recorded. California and Florida are also reporting average highs.
Stunning iPhone 12 video shows Apple’s flagship in all its glory
CarKey will let users unlock, start and lock their cars without fumbling through their bag or pockets for a physical key. The tech giant says it won't get data on when you access your auto or who you share your vehicle keys with either.
Despite the grim news from Texas, Florida and elsewhere, U.S. President Donald Trump said the United states was coming back from the coronavirus crisis, which has halted large parts of the economy and left millions jobless.
Texas and Florida, both with Republican governors who had resisted prolonged lockdowns, have announced new restrictions on bars.
Newsom has paused allowing counties to further reopen their economies in response to rising COVID-19 hospitalizations.
In Florida, DeSantis claimed when the median age for people infected with the virus in March was in the 60s, in the past two to three weeks it really is dropped to men and women in their early 30s.
Experts are still encouraging the public to social distance and wear masks.
Texas had been at the forefront of states peeling away restrictions created to control the pandemic, allowing bars to reopen in May.
"If I could go back and redo anything, it probably would have been to slow down the opening of bars, now seeing in the aftermath of how quickly the coronavirus spread in the bar setting", Abbott told the KVIA news station in El Paso. "The more that we all adhere to these suggestions, the safer our point out will be and the more we can open up up Texas for company".