NEW ORLEANS — Louisiana reported by far its largest number of new coronavirus cases in a 24-hour period Tuesday afternoon, with reported infections and deaths each jumping about 30 percent, as state leaders renewed calls for residents to comply with social distancing rules, and crackdowns on violators continued.

The "very sobering numbers" brought the state's total number of cases to 5,237, and 239 covid-19 patients have died, Gov. John Bel Edwards (D) said at a news conference. That is an increase of 1,212 cases and 54 deaths over what the state reported Monday. The city of New Orleans had 1,834 total cases and 101 deaths.

The new data pushed up the estimated date when the New Orleans region could run out of ventilators to April 4, and advanced the date when hospital beds in the region may be filled to April 7, the governor said.

Edwards offered one caveat to the numbers: State health officials said 90 percent of the new cases were based on tests processed by private labs, and officials have been unable to pin down whether the spike in cases is partly because of a sudden rush of reporting of tests that could have been collected many days ago. Nonetheless, Edwards and assistant health secretary Alexander Billioux did not minimize their concern at the new figures.

"It also reaffirms to me that we have yet to see any evidence that we are beginning to flatten the curve," Edwards said. He added that since March 26, the number of covid-19 patients in hospitals and the ones on ventilators have both doubled.

The dwindling ventilator supply is a key concern. The state has ordered 14,000 in the past few weeks and received just 292, Edwards said. Another 150 that President Trump had promised in a videoconference call Monday were due to arrive later Tuesday or Wednesday — enough to add a day to the state's capacity. "Certainly it is not everything that we need, but it will help," Edwards said.

To address hospital bed scarcity, Edwards announced that he is doubling the number of beds that will be available at the Morial Convention Center to 2,000. Those beds will be available to recovering covid-19 patients who no longer need to occupy a hospital bed but aren't quite well enough to go home. The purpose is to be able to free up hospital beds for new patients more quickly.

Still, the best way to preserve the capacity of the health-care system is for residents to stay home and avoid exposure, Edwards and Billioux urged. Earlier Tuesday, a controversial pastor who held several large religious gatherings over the past two weeks was issued a misdemeanor summons on six counts of violating an executive order from the governor prohibiting such events, according to the police chief in the town of Central, just outside Baton Rouge.

The Rev. Tony Spell leads the Life Tabernacle Church. This past weekend more than 550 parishioners attended his service, with twice as many having attended the previous weekend, Spell told a local news reporter. He indicated he would continue to hold them regardless of the health risks, forcing the hand of law enforcement, Central Police Chief Roger Corcoran said in a statement.

"Instead of showing the strength and resilience of our community during this difficult time, Mr. Spell has chosen to embarrass us for his own self-promotion," Corcoran said in the statement. "This is not an issue over religious liberty, and it's not about politics. We are facing a public health crisis and expect our community's leaders to set a positive example and follow the law."

Spell did not immediately respond to a voice message left by The Washington Post at his church.

Asked by a reporter at the briefing about the case, Edwards said: "It is very unfortunate that any leader of any kind — business leader, community leader, faith leader — would choose and make the conscious decision to violate what is a legal order and one that is imperative for public health."

The rise in cases is probably a preview of more to come until Louisiana reaches its peak, which some models project for the second week in April, according to health experts.

"I do know the [test] results are coming in erratically, but we do have 5,237 cases and 239 deaths," said Patty Kissinger, professor of epidemiology at the Tulane University School of Public Health and Tropical Medicine. "That's a lot; that's astounding. There's obviously very wide community spread. It's hit almost every parish" in the state.

Warner Thomas, chief executive of Ochsner Health, which operates five hospitals in the New Orleans area, said the new numbers are not surprising, and he expects to see continued "growth in patients over the next couple of weeks as we head towards the peak."

Bed capacity and ventilators continue to be the most pressing issues, he said. Out of 1,460 patients staying in the hospital, 820 are in for covid-19 and their average lengths of stay range between four days to two weeks. Ochsner is expanding the number of ICU beds by 110, but the volume of cases still presents a challenge, Thomas said. Typically, 30 percent of intensive care patients are on ventilators. That number is now closer to 90 percent.

The good news, he said, is that they have discharged 400 patients over the past several weeks who tested positive and are now on the mend.