As of Thursday, the state had 433 people hospitalized with the virus. Its average positive test rate over the past seven days is at 2.3 percent, which Mr. Lamont said was the lowest rate in nearly four months.

“We’re beginning to get a handle on what works,” he said, pointing to the decline.

Still, over the past week, Connecticut has reported an average of 22 new virus cases a day per 100,000 people, a rate that is the 10th highest per capita among all states.

The United States as a whole is averaging 19 new daily cases per 100,000 people. Federal health officials, including the head of the Centers for Disease Control and Prevention, have urged governors not to relax their rules, warning that the country may be leveling off at a relatively high number of daily virus cases.

But Mr. Lamont said that he did not believe that the capacity limits on businesses were having a significant enough effect on curbing the virus that they needed to remain in place.

“It’s not so much a question of how you adjust the dial and go ‘capacity up 10 percent’ or ‘down 10 percent,’ or whether you have a curfew for two weeks or four weeks, and then you go back,” Mr. Lamont said. “I think we’re finding what works is wearing the mask, social distancing and vaccinations.”

Mr. Lamont’s announcement reflected decisions by other states to loosen virus-related restrictions as vaccination programs were ramping up and the number of new cases were starting to plateau. Throughout the pandemic, officials have had to adjust restrictions, finding a balance between safety, economic concerns and political pressure.

The governors of New York and New Jersey, both also Democrats, with whom Mr. Lamont has collaborated significantly on the pandemic response, have raised capacity limits in businesses, including restaurants, in the past month. Both of those states have been reporting new cases at the highest rates in the country.