Gov. Tom Wolf is not yet considering relaxing any of the state’s tightened restrictions on restaurants and bars, he said Tuesday, saying that keeping coronavirus protocols in place will be the fastest way to get to a fuller reopening.

A day after giving school districts specific guidance on reopening based on local virus transmission data, Wolf said the state was not planning to transfer that type of localized reopening to other sectors, such as the food and drink industry.

“There’s a difference between elective things that we do and central things that a society needs to do,” he said. “We need to get our kids back to school. We need to make sure they get an education. That’s our first priority.”

Wolf said his administration would give the Pennsylvania Interscholastic Athletic Association guidance about fall high school sports, which remain in limbo, based on area-specific virus transmission data.

Like officials in Delaware and elsewhere, the Wolf administration has said that keeping the spread of the coronavirus low and pushing it lower will provide the best chance for schools to successfully reopen. The way to do that, they say, is for residents and businesses to continue to follow safety protocols and abide by the restrictions designed to prevent transmission.

“All these other things will allow us to get back to life as normal as quickly as we can,” Wolf added Tuesday, “and that includes restaurants and bars, sports.”

What returning to life as normal means remains an open question more than five months into the pandemic. On Tuesday, the world surpassed 20 million cases of infection by the virus; five million of those are in the United States. Fall college football was canceled by two of the country’s largest conferences, the Big Ten and the Pac-12.

The University of Pennsylvania became the latest college in the region to change course for the fall semester, announcing it will hold only remote classes and host almost no students in its dorms.

Pennsylvania officials said they expected a Bethlehem-based manufacturer working on a rapid, self-administered coronavirus test would “be moving fairly quickly” to submit it to the Food and Drug Administration for emergency authorization.

Health Secretary Rachel Levine expressed optimism about the potential for such a test to help the state’s nursing homes, schools, prisons, and other arenas — particularly as turnaround times for commercial lab results continue to be as long as two weeks.

“This would be a game-changer,” she said.

The company, OraSure Technologies, which has an FDA-approved rapid Ebola test on the market, is working on two coronavirus tests: a diagnostic that they say could be administered and read at home and an antibody test that they say would be reliable. (The accuracy of others has been questioned.)

The company’s CEO, Stephen S. Tang, said he believed it could be on the market by the end of the year. OraSure is set to receive more than $1 million in state grants and tax credits upon adding a planned 177 new employees.

Pennsylvania reported 828 new virus cases and 35 deaths on Tuesday. The state’s moving seven-day average for the number of new cases identified daily was 753 and had remained roughly steady over the last five days.

In Philadelphia, the city continues to see declining rates of newly confirmed coronavirus cases, which officials said Tuesday was a reason for optimism that efforts to control the pandemic are working and a sign that residents should continue to wear masks and practice social distancing.

“As of today, all the trends of this are in the right direction. All the trends are good,” Public Health Commissioner Thomas Farley said in a virtual news conference. “We want to maintain this momentum. We don’t want to go backward.”

The city reported 145 new cases on Tuesday. For the week that ended Saturday, the city saw an average of 105 new cases per day, which is down from 123 per day the week before and 166 the week before that.

Fifty-nine percent of new cases confirmed Tuesday were in people under 40 years old, Farley said.

Severe outcomes from the virus are also on the decline, Farley said. The city reported only one death from the virus on Tuesday. In April, Philadelphia saw more than 250 people die.

He cautioned that the positive trend does not mean older Philadelphians or those with underlying medical conditions should ease safety precautions. The city next week will mail postcards to about 14,000 residents who have been identified as being at high risk of experiencing severe illness if they contract the virus, Farley said.

“There really is an extra risk for people who are medically vulnerable,” he said. “Avoid contact without masks, even with your relatives and caregivers who are out and about.”

New Jersey reported 498 new cases, and its seven-day average for daily cases was 358. It reported 14 newly confirmed deaths, half of which were not from August.

Hawaii, South Dakota, and the U.S. Virgin Islands were added to New Jersey’s travel advisory, which asks residents traveling from states with high infection rates to quarantine for 14 days. Ohio, Rhode Island, Alaska, and New Mexico were removed from the advisory list.

Travelers from 31 states, plus Puerto Rico and the Virgin Islands, are still asked to quarantine.

“To protect the steady progress we’ve made on our road back, we need everyone who has traveled to one of these impacted states or territories to practice self-responsibility,” Gov. Phil Murphy said in a statement. “I strongly encourage all individuals arriving from a hot spot to proactively get a COVID-19 test and self-quarantine to reduce transmission across our state.”

Staff writers Sean Collins Walsh, Kristen A. Graham, and Rob Tornoe contributed to this article.

Correction: This article has been changed to correct the virus infection total for the United States.