First, Indonesia’s agriculture minister promoted wearing a necklace containing a eucalyptus potion to cure the coronavirus. Not to be outdone, the governor of Bali, a popular resort island, pushed his own remedy: inhaling the steam from boiled arak, a traditional alcohol made from coconuts.

So-called influencers and self-styled experts have also pushed their own quack cures and misinformation on Indonesian social media, including a widely spread rumor that popular infrared thermometer guns cause brain damage.

As Indonesia steadily loses ground to the pandemic, the government has had difficulty delivering a consistent, science-based message about the coronavirus and the disease it causes, Covid-19.

As of Friday, Indonesia had reported more than 108,000 cases and more than 5,130 deaths, surpassing China in both categories.

Yet even in hard-hit provinces, as many as 70 percent of people go without masks and ignore social distancing requirements, according to the government, often crowding into shops and markets and hanging out at busy cafes and restaurants.

Indonesia is not the only country battling misinformation or whose leaders have promoted quack remedies. The World Health Organization has called the ubiquity of hazardous false information an “infodemic.”

In Kenya, the governor of Nairobi has pushed cognac as a miracle cure. President Trump has continued to promote hydroxychloroquine, a drug used for treating malaria, as a coronavirus remedy despite medical evidence to the contrary. He has even suggested that an “injection inside” the human body with a disinfectant like bleach could help combat the virus.

But Indonesia is unique because of its large population, expansive geography across thousands of islands and mix of cultural identities. It would be difficult enough for the government to implement a clear and unified plan for combating the virus, but matters have been made worse by the promotion of muddled and often dangerous information.

The country’s president, Joko Widodo, had initially downplayed the pandemic and has delivered mixed messages. He admitted in March that he had misled the public about the virus to prevent a panic. After that, he was slow to close businesses and schools and to limit travel, but was quick to lift restrictions even as cases continued to rise.

In May, he said Indonesia should learn to live with the virus. A month later, however, he threatened to fire cabinet ministers for not doing more to bring the pandemic under control.

This month, he called for a national campaign to promote better discipline in social distancing, mask wearing and hand washing.

In the absence of a unified message from the national government, local officials and opportunists have filled the gap.

One official who has promoted a questionable remedy is the agriculture minister, Syahrul Yasin Limpo. He told reporters this month that a ministry laboratory had developed a potion made from eucalyptus that when worn on a necklace could kill 80 percent of virus particles in half an hour.

“From 700 species of eucalyptus, our lab test results showed that one kind could kill the corona,” he said. “We are certain. We will produce it next month.”

His claim was quickly contradicted by health experts, including the head of the laboratory that developed the aromatic potion, who said it was not effective against the coronavirus. But that didn’t stop others from promoting it.

A popular singer, Iis Dahlia, met with Mr. Joko as he sought to recruit celebrities to help in his health campaign. Soon after, she informed her 12 million Instagram followers that she was proud to be wearing the amulet.

“This eucalyptus necklace,” she said, “makes me feel safe and protected from the virus.”

In Bali, the governor, I Wayan Koster, has promoted a local treatment: inhaling the steam of boiled arak, a traditional alcoholic beverage. As if to stay on trend, he too recommends adding a dash of eucalyptus oil.

The governor, who has a Ph.D. in education and described himself as a former “researcher,” told a news conference last week that nearly 80 percent of those who inhaled the concoction tested negative sooner than would have been expected.

The treatment has not been subjected to scientific testing, but he said he hoped that Bali could patent and produce it.

The government’s top coronavirus spokesman, Wiku Adisasmito, urged the public to follow health guidelines and not to rely on superstition and half-baked treatments, even when they emanate from public officials and celebrities.

“At times of emergency, we all need honest, scientifically based, real facts to bring us hope, calm and clarity,” said Mr. Adisasmito, a University of Indonesia health policy professor.

Jusuf Kalla, a former vice president who now heads the Indonesian Red Cross, said the country got off to a slow start in fighting the pandemic in part because the health minister, Terawan Agus Putranto, minimized its severity.

“Until March, Minister Terawan was like Trump, saying, ‘Oh, this is only a simple flu,’” Mr. Kalla said. “But now, Minister Terawan is very realistic. Ministers and governors are trying to come up with solutions in an uncertain situation. It is trial and error.”

Indonesia is the world’s largest Muslim-majority country, and some citizens and officials have leaned on their faith to promote cures and guide their understanding of the disease.

On Lombok Island, a top official suggested that niqabs, loose Islamic veils worn by women, were as effective in preventing the spread of the virus as snug-fitting medical face masks.

“The advantage of the niqab is more ease in breathing,” Suhaili Fadhil Thohir, the regent of Central Lombok, explained in an interview.

Nevertheless, the Covid task force for the province, West Nusa Tenggara, continues to call for face masks, said Artanto, a police spokesman and task force member.

“The regent still wears a mask, not a niqab,” said Mr. Artanto, who like many Indonesians uses one name. “We keep educating people to wear a mask.”

For many Muslims, the Covid-19 burial protocol of wrapping the body tightly in plastic and burying it in a designated cemetery has been difficult to accept. By tradition, Muslim family members wash the body of the deceased and wrap it in cloth for burial.

The authorities say there have been many cases around the country of families rejecting doctors’ warnings and taking Covid-positive bodies home for burial.

In Mataram, Lombok’s main city, relatives of a woman who died in a motorcycle accident this month refused to believe doctors who said she had tested positive.

About 100 men stormed into Mataram’s government hospital to claim the body. Officers tried to explain the importance of the burial protocols. But they were badly outnumbered, and the men took the body, put it in a taxi and drove away.

“It happens all over Indonesia,” Mr. Artanto said. “Their understanding as people who live in the village is different from those of us who live in the city.”

Mr. Adisasmito said that Islamic burial traditions were deeply ingrained, and that it was hard for people to accept that they must change. He likened it to Americans who refuse to wear a mask because it obstructs their “pre-pandemic liberty, habits and way of life.”

“We live in a diverse globe,” he said, “and different communities have distinctive values that they hold on to.”

Muktita Suhartono and Dera Menra Sijabat contributed reporting.