SYDNEY—Australia used a combination of its island geography and local lockdowns to eliminate the coronavirus earlier in the pandemic. But the Delta variant is so infectious that some Australian leaders believe it will be impossible to get down to zero cases again.

Australia this week reported the highest number of cases since the pandemic began. There were 747 new local cases of the virus across the country on Wednesday, beating the previous daily high of 716 in July of last year, according to the latest numbers from Our World in Data. The country’s two biggest cities, Sydney and Melbourne, are in lockdown, as is the country’s capital, Canberra.

“To assume that forevermore there’ll be zero cases around Australia is, I think, an assumption that nobody can really make at this stage,” said Gladys Berejiklian, the premier of New South Wales state, which includes Sydney. “We can’t pretend that we’re going to be zero cases around Australia of Delta.”

Although small by global standards, Australia’s Delta outbreak is a case study in how quickly it can spread in a lightly vaccinated population with low immunity. The vaccine rollout has increased recently but just 22% of the population has been fully vaccinated, compared with more than half in the U.S. and the U.K., according to Our World in Data.

As the Delta variant sweeps the globe, scientists are learning more about why new versions of the coronavirus spread faster, and what this could mean for vaccine efforts. The spike protein, which gives the virus its unmistakable shape, may hold the key. Illustration: Nick Collingwood/WSJ The Wall Street Journal Interactive Edition

Not all of Australia’s leaders are ready to give up on elimination, at least while vaccination rates remain relatively low. Leaders of Australia’s states had agreed to a Covid-19 exit strategy that called for the virus to be aggressively suppressed until at least 70% of the adult population had been vaccinated.

Leaders in Queensland and Western Australia states, where there hasn’t been as much local transmission of the Delta variant as in other states, say they will continue to try to keep local cases close to zero for now. Australian troops will be deployed to the border between Queensland and New South Wales after Queensland requested help enforcing a travel ban, according to local media.

“The national plan at the moment is you minimize or eliminate the spread of Delta,” said Mark McGowan, who leads Western Australia state. “That’s what New South Wales should be doing.”

The outbreak began in mid-June in New South Wales, Australia’s most populous state, where authorities believe a driver contracted the virus from an international flight crew. Since then, more than 10,000 people in the state have been infected with the Delta variant and there have been 65 deaths, according to the New South Wales government. Another 644 local cases were reported in the state on Friday.

The outbreak is probably the beginning of the end of Australia’s strategy to keep out the virus, said Stuart Turville, an associate professor and virologist at the Kirby Institute at the University of New South Wales. Other countries that sought to aggressively suppress the virus, including China and South Korea, are also struggling to get cases to near zero, he said.

“It’s not going away globally,” he said. “I want to get to zero, don’t get me wrong. But I think the biology is not in our favor.”

Officials in Sydney said Friday they will extend the city’s lockdown and further tighten restrictions to limit hospitalizations and deaths while more people get vaccinated. The two-month lockdown was scheduled to lift at the end of August but will now run at least through September.

“What this is about is buying us time,” said Kerry Chant, the chief health officer in New South Wales state.

The vaccine rollout has been slow in part because the AstraZeneca PLC vaccine—which unlike some of the others can be made in Australia—was deemed inadvisable for people under 60 due to fears of rare blood clots. Australia later changed that advice, urging people over 18 to get the shot. Officials have said millions of doses of the Pfizer Inc. -BioNTech SE vaccine and the recently approved Moderna Inc. shot will arrive in the coming weeks and months.

Many of the cases in the Sydney outbreak have been people under 40, who until recently weren’t eligible to be vaccinated as authorities focused on older people more at risk for severe disease. Local authorities in Sydney recently began vaccinating high-school students and adults under 40 in hot spots with the Pfizer vaccine.

Australia’s federal government is also playing down the likelihood that the virus can be eliminated.

“It’s a fallacy to talk about the elimination of Covid,” Treasurer Josh Frydenberg said in a television interview Thursday. “We are going to be living with Covid for a number of years to come.”

Epidemiologists and officials say measures that eliminated earlier strains don’t work with Delta because the variant is so contagious. Lockdowns can still be effective but only if put in place almost immediately—a lesson that has taken some time to learn.

In neighboring New Zealand, officials placed the country into lockdown this week after finding one case that authorities traced to a traveler from Sydney. Cases in New Zealand have since climbed to 31 but the government’s commitment to its zero-Covid-19 strategy hasn’t changed.

In Australia’s Victoria state, which includes locked-down Melbourne, Premier Daniel Andrews said the Delta outbreak there isn’t unbeatable yet but is proving to be a bigger challenge than earlier strains.

Containing the outbreak is “still within our reach but so too is deteriorating to the point where Sydney is,” said Mr. Andrews, whose state recorded 55 new cases Friday. “Then the only choice you’ve got is to vaccinate your way out of it.”

—Stephen Wright in Wellington, New Zealand, contributed to this article.

Write to Mike Cherney at mike.cherney@wsj.com