By Tedd Mann and David Hall

New coronavirus cases in the U.S. rose above 44,000 for the first time in nearly a week, with elevated numbers continuing in parts of the Midwest, while the total number of cases world-wide passed 30 million.

With a number of vaccines in various stages of development, some companies are sketching out possible time frames for data to emerge from drug trials.

Moderna Inc. Chief Executive Stéphane Bancel said a large study could yield a preliminary answer about whether the company's Covid-19 vaccine works safely as early as October, though more likely in November. Pfizer Inc. Chief Executive Albert Bourla, in recent television interviews, also gave an end-October time frame for key data from final-stage trials of its vaccine, being developed with partner BioNTech SE.

Even if the trials provide positive results this fall, most people wouldn't be able to get vaccinated until next year because supplies will be limited early on.

The federal government's slow start to its distribution plans, along with other issues, could hamper efforts to get the shots quickly to health-care workers and others at high risk of infection, according to state and industry officials. Some states might not initially get all the supplies they were expecting, or have all the freezers needed to safely store their allocation, the officials said.

"All those unknowns will have an impact on who will be vaccinated and how," said Dr. Eddy Bresnitz, medical adviser to New Jersey's health commissioner on the Covid-19 response.

Cases:

The U.S. reported more than 44,000 new cases for Thursday, as the death toll approached 198,000, according to data compiled by Johns Hopkins University. Wisconsin, one of several Midwest states where numbers are running high compared with the Spring, reported more than 1,600 cases for Thursday, its highest daily count to date, according to Johns Hopkins.

Earlier this week, Wisconsin Gov. Tony Evers warned residents that cases would continue to increase "until folks decide to take this seriously." Over the past week, the percentage of positive tests, known as the positivity rate, ticked up to 14.9% in Wisconsin. Nationally, the seven-day moving average positivity rate was 4.9%, according to data from Johns Hopkins.

In all, 14 states reported more than 1,000 new covid cases on Thursday, led by Texas, with 4,543 new cases. Nationwide, states reported 870 deaths attributed to Covid-19, bringing the U.S. death toll from the pandemic to almost 198,000 people.

But there were signs of easing in some states hit hard over the summer. In the past week, the seven- and 14-day case averages have remained near 2,700 in Florida and 3,500 in California. For most of July, California was averaging more than 8,000 new cases a day and Florida more than 10,000. On Thursday, Florida reported 3,255 new cases and California reported 3,716 according to data from Johns Hopkins.

Through Thursday, there were 278,311 new cases of Covid-19 reported over the preceding 7 days, according to data from Johns Hopkins, a slightly larger weekly increase than the week before when 246,084 cases were recorded.

As state officials prepare for the possibility of an autumn surge of new infections, some hospitals say they will be better prepared to handle an influx of new patients than they were at the outset of the pandemic, thanks to deeper stockpiles of equipment and better understanding of how to treat the disease. Medical officials are stocking up on equipment like masks, and are preparing to use antiviral and steroid medications that studies suggest have helped patients recover from Covid-19.

Texas: Covid-19 restrictions in Texas will now be regional and driven by hospitalizations, Gov. Greg Abbott said Thursday. Starting Monday, businesses will be allowed to expand capacity from 50% to 75% except in parts of the border and southern Gulf Coast region, which has been hardest hit by the virus. Bars, however, will stay closed for now.

New York: Safety concerns have again delayed the restart of in-person learning in New York City. Mayor Bill de Blasio said it would begin in phases according to grade level. Preschool children will start on Monday. Many students in kindergarten through eighth grade will start Sept. 29. High-school students and some middle-school students will start Oct. 1.

World

Brazil: The pandemic has interrupted therapy sessions and other treatment for children born with birth defects caused by the Zika virus. Health authorities suspended physiotherapy for more than 3,500 children who were born with abnormally small heads and other disabilities after being infected with Zika while in the womb. Families are concerned that breathing problems linked to Zika could make those children more vulnerable to serious complications if they contract Covid-19.

India: More than 96,000 new cases were reported, pushing the country's total above 5.2 million, according to the Ministry of Health and Family Welfare. India's death toll rose by 1,174 to 84,372. Its total caseload is the second largest after the U.S. Along with Brazil, the three countries make up more than half of the global cases recorded so far. Total global deaths have now reached 946,673, according to Johns Hopkins data.

Guam: The U.S. territory reported 32 new cases late Thursday, bringing the total on the island to 2,045. The number of intensive-care patients has risen to 19, stretching the local hospital system.

Japan: Tokyo logged 220 new cases, the most in six days. The city is set to be included in the government's tourism promotion program starting Oct. 1. The $10 billion campaign, which subsidizes travel costs, was launched in late July, but excluded trips to and from Tokyo because of high levels of infections at the time. Nationwide, Japan reported 490 new cases, in line with recent levels, and nine additional deaths.

Australia: Victoria state reported 45 new cases and five deaths. New South Wales, home to Sydney, had six cases. Several states agreed to lift caps on international arrivals to help some 24,000 Australians stranded overseas return to the country. Currently, flights are limited by the number of available spots at hotels used for mandatory quarantines.

U.K.: Britain's health minister said the spread of the virus was accelerating. Matt Hancock said hospital admissions are doubling every eight days, but speaking on Sky News he declined to say if the country would introduce a second national lockdown after seeing a sustained rise in daily cases. So far, governments in England, Scotland and Wales have applied targeted restrictions to contain the virus.

Israel: The country began a second nationwide lockdown Friday afternoon. Thousands of policemen and soldiers are being deployed to enforce the sweeping closures, taking place during Jewish new year celebrations and which are widely unpopular. New daily cases are hovering at around 5,000 a day, making Israel one of the countries with the worst infection per capita rates in the world.

Write to Ted Mann at tedd.mann@wsj.com and David Hall at david.hall@wsj.com