Hong Kong announces its toughest social-distancing rules yet as cases reach record highs.

Hong Kong will institute its tightest social-distancing rules since the start of the pandemic to curb its largest coronavirus outbreak so far, as a wave of Omicron cases has raised questions about how long the city can continue its strict Covid-control policies.

Hong Kong will require hair salons and places of worship to close for two weeks starting Thursday, and no more than two households will be allowed to meet in private, Carrie Lam, Hong Kong’s chief executive, said on Tuesday. Public gatherings will be limited to two people.

Shopping malls, grocery stores and markets will join the list of public places where visitors must register with an official contact tracing app. People visiting those sites, which include restaurants, will have to prove they have been vaccinated. Fines for not following mandatory testing orders will be doubled to nearly $1,300.

The city of 7.5 million has largely managed to avoid the worst of the pandemic, recording 213 Covid deaths over the past two years. But the spread of the highly transmissible Omicron variant since late December now threatens to overwhelm Hong Kong’s aggressive contact tracing and quarantine efforts. Since last week it has set several daily highs for new case totals, with more than 600 added on Monday and again on Tuesday.

The surging number of cases has forced the city to stop hospitalizing all Covid patients. On Tuesday it began sending some people with few or no symptoms to the government quarantine center at Penny’s Bay. And some close contacts who were previously required to go to Penny’s Bay will now be allowed to quarantine at home.

Mrs. Lam has resisted suggestions that the latest wave of cases will force Hong Kong to abandon its strategy, which she calls “dynamic zero Covid.”

“In our fight against the epidemic we need to stand by a philosophy, otherwise we will see measures being change all the time,” she said on Tuesday. “So at this moment, we will stand by the dynamic zero containment strategy.”

The risk to older people is of particular concern, Mrs. Lam said, because less than half the population over age 70 have been vaccinated. “The risk is increasing because there are more cases in residential homes and among their workers,” she said.