By Allison Prang and David Hall

The U.S. reported more than 34,000 new coronavirus cases, higher than the daily totals of the past few days even as testing slowed over the holiday weekend.

For both Monday and Tuesday, the U.S. logged fewer than 30,000 new cases. Testing, however, declined over Labor Day weekend and afterward, according to the Covid Tracking Project. The U.S. conducted fewer than 590,000 tests daily Monday through Wednesday compared with last week, when daily tests topped as much as 900,000.

"If there is a Labor Day bump in cases, we probably won't be able to detect it until late September," Christine Ekenga, assistant professor of public health at Washington University in St. Louis, said in an email Wednesday.

The seven-day average of new cases was about 35,394, according to a Wall Street Journal analysis of data from Johns Hopkins University. That is the lowest it has been since June 26.

Travel: The U.S. government on Monday will stop requiring incoming passengers from certain countries to undergo a health screening at the airport, the Centers for Disease Control and Prevention said, adding the U.S. now has a better understanding of how Covid-19 spreads and believes those screenings have "limited effectiveness."

In a statement, the CDC said the screenings don't blunt transmission of the virus because passengers may not yet have symptoms or may be asymptomatic.

The federal government also no longer will direct all incoming passengers from certain countries to arrive at one of 15 airports. Passengers arriving from China, Iran, certain European countries, the U.K., Ireland and Brazil have been required to undergo health screenings upon arrival.

The CDC said it instead will prioritize educating passengers about the transmission of the virus before, during and after a flight and collecting contact information electronically to avoid long lines. The agency also said it would prioritize "potential testing" but didn't give more details about how testing might be expanded.

Economy: Unemployment claims in the U.S. remained steady last week compared with a week earlier, at more than 880,000, the Labor Department said Thursday. Claims have fallen since March, but remain at historically high levels. Stocks rose in morning trading.

The U.S. Senate will take up a pared-back coronavirus relief bill on Thursday, which most Republicans are expected to support. Democrats are set to block the legislation since they say it doesn't go far enough.

The bill doesn't include some provisions from Republicans' earlier plan, such as an additional $1,200 stimulus check for many Americans. It calls for about $300 billion in new spending.

California: Gov. Gavin Newsom said that, by one estimate, a "jaw dropping" 44% of small businesses in the state believed they might be forced to close because of the pandemic. He signed three bills Wednesday aimed at helping them, including one that will give up to $100 million in tax credits for small businesses that hire or rehire employees in the next three months.

New York City: Indoor dining at restaurants will restart -- with limited seating -- in the city at the end of September, New York Gov. Andrew Cuomo said Wednesday, lifting a nearly six-month ban. Restaurants must cap capacity at 25% and abide by other restrictions.

West Virginia: Gov. Jim Justice said that while the state hasn't seen many deaths compared with others, new data was concerning. "We are absolutely getting worse by the day, and this situation right now is very critical," he said, citing the daily positivity rate of 7.78%. The reproduction rate is at 1.35, he said. "It's the worst in the nation," he said. "We have got to do any and everything we can to do better."

Cases and deaths: The U.S. reported 34,256 new cases for Wednesday, according to data compiled by Johns Hopkins University, up from 26,387 for Tuesday. The death toll rose by more than 1,200 to nearly 191,000. The global death toll surpassed 903,000.

Vaccines: An independent committee is reviewing the potential safety concern that led to a pause in AstraZeneca PLC's clinical trials of an experimental Covid-19 vaccine. Chief Executive Pascal Soriot on Thursday said, "We could still have a vaccine by the end of this year, early next year."

Health experts say it is likely that more than one vaccine could succeed in clinical trials and become available in the near future. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, told The Wall Street Journal "it's quite conceivable, if not likely, that you're going to have multiple candidates that'll get over the finish line that will actually be good enough to be approved for production and use."

World

India: The country reported a record single-day surge in both cases and fatalities, with 95,735 new infections and 1,172 deaths, according to data from the Health Ministry. India's total number of confirmed cases surpassed 4.46 million, the second-highest level behind the U.S., according to Johns Hopkins, while the death toll topped 75,000. Medical experts have said the easing of most virus-related restrictions, along with lax adherence to social-distancing rules, has likely contributed to the rise in infections.

Guam: Gov. Lou Leon Guerrero extended a stay-at-home order for the island until Sept. 18. The U.S. territory reported 45 new cases. Guam also launched a phone app to improve contact tracing.

Japan: The Japan Sumo Association reported 18 new cases Thursday at a sumo stable after a wrestler tested positive a few days earlier. Several sumo wrestlers have been infected with the virus over the course of the pandemic. A 28-year-old wrestler died from Covid-19 in May. Nationwide, Japan reported 510 new cases and 13 deaths, in line with recent levels.

South Korea: The country reported 155 new cases, the eighth day in a row that infections remained below 200. The latest numbers show improvement after cases surged in mid-August due to an outbreak largely tied to churches. Tightened social-distancing measures are set to remain in place until at least Sept. 20.

Australia: Victoria state reported 51 new cases and seven deaths, pushing the state total death toll above 700, while nationally there have been 788 fatalities. New South Wales, home to Sydney, recorded seven new cases, including two linked a growing cluster tied to emergency rooms at two hospitals.

U.K.: The British government prohibited gatherings of more than six people in England from next Monday. It is the latest country in Europe to reimpose restrictions on daily life amid a surge in cases. Newly detected infections appear overwhelmingly mild: Hospitalizations and deaths have remained more or less stable at low levels in most countries. But the worry is that without firm action now, the infection could percolate by winter to higher-risk groups including the sick and the elderly.

Austria: Austria joined the ranks of European countries seeing a surge in infections, reporting 664 new cases Thursday, 387 of them in Vienna. It was the highest increase since late March.

Indonesia: The country reported a record 3,861 new infections, increasing its total caseload to over 207,000, with 120 new deaths. Total fatalities stood at 8,456, the highest in Southeast Asia, where the Philippines also saw an uptick in new cases, reporting 3,821 Thursday, the highest in 11 days.

--Rebecca Ballhaus contributed to this article.

Write to Allison Prang at allison.prang@wsj.com and David Hall at david.hall@wsj.com