Convincing residents of the importance of Internet access — to apply for jobs, do research, take classes and get information on government services — was one of Google’s primary challenges here. The service is currently being offered only here and in Kansas City, Kan. About 25 percent of homes in both cities do not have broadband, and 46 percent of blacks do not use the Internet.

Qualifying neighborhoods will get Internet service with speeds of up to a gigabit per second — 100 times faster than the average broadband connection — for $70 a month. Google is also offering a television service along with Internet for $120 a month. Schools, libraries, hospitals and other institutions in areas that qualify would receive gigabit connections for free.

But the feature most attractive to low-income areas is Google’s offer of a free 5-megabit Internet connection for 7 years, but which requires a one-time $300 construction fee.

As of Sunday evening, only about 32 percent of people in the neighborhoods that qualified for Google Fiber were black, while just over 54 percent were white, according to Mr. Beveridge.

With almost all of Kansas City, Kan., including low-income areas, achieving their sign-up goals, Google’s focus over the weekend was here in Missouri, where it worked with community groups to register people.

The dividing line of Troost “certainly predated us,” said Kevin Lo, the general manager of Google Access, which oversees the Fiber operation. “It’s unrealistic to expect that we can, in six weeks’ time, close the gap.”

Yet Mr. Lo said helping close the digital divide was “absolutely a core part of our mission.”

Google planned to announce on Monday that neighborhoods that did not qualify this time would have another opportunity to do so, though it did not say when. It also said it would offer grants to community groups in Kansas City to promote digital literacy.