In buying the Public Interest Registry, Ethos Capital would acquire the rights to run dot-org and collect annual fees from the nearly 10.5 million registered dot-org names, held by both nonprofits and domain-name speculators. Those yearly fees are $10 to $20 on average, but can be far higher for big sites that buy several names to protect their brand and get added services like security against online attacks.

Opponents of the private-equity sale said they feared that to make an attractive profit on its pricey deal, Ethos Capital would have to raise prices, cut expenses, skimp on service — and most likely sell users’ data.

Ethos Capital said those concerns were unfounded.

In a blog post in December, Erik Brooks, the firm’s founder, said that “we understand that change brings uncertainty and concern,” which was reflected in “alarmist statements.”

Ethos Capital, Mr. Brooks said, wants to invest in dot-org “for the reputation of the platform and the values it represents in the marketplace.” He said his firm planned to build on that asset.

Big price increases have been a major concern for critics of the deal. When ICANN renewed the 10-year contract with the Public Interest Registry last year, it removed a price cap that limited price increases to 10 percent a year at most. That move was part of a broader ICANN policy to ease price controls across all internet domains.

Ethos Capital has pledged to adhere to the 10 percent cap, though it would have no contractual obligation to do so. In blog posts, the private equity firm said it planned to invest in new services and clamp down on spam, security attacks and other abuse launched from some illicit dot-org domains.

Some nonprofits worry that any cleanup effort could result in censorship, even if inadvertently. As the owner of the registry for dot-org, Ethos Capital would manage the acceptable business practices and conduct for dot-org domains. The same freedoms that open the door to extremist groups on some dot-org sites, nonprofit leaders say, also help protect free speech on public-interest dot-org sites in developing countries with authoritarian governments.