WASHINGTON, Oct. 28 The Federal Communications Commission, hoping to reduce the rising costs of cable television, is preparing to strike down thousands of contracts this week that gave individual cable companies exclusive rights to provide service to an apartment building, the agency’s chairman says.

The new rule could open markets across the country to far-ranging competition. It would also be a huge victory for Verizon Communications and AT&T, which have challenged the cable industry by offering their own video services. The two companies have lobbied aggressively for the provision. They have been supported in their fight by consumer groups, satellite television companies and small rivals to the big cable providers.

Commission officials and consumer groups said the new rule could significantly lower cable prices for millions of subscribers who live in apartment buildings and have had no choice in selecting a company for paid television. Government and private studies show that when a second cable company enters a market, prices can drop as much as 30 percent.

The change, which is set to be approved Wednesday, is expected to have a particular effect on prices for low-income and minority families. They have seen cable prices rise about three times the rate of inflation over the last decade. A quarter of American households live in apartment buildings housing 50 or more residents, but 40 percent of households headed by Hispanics and African-Americans live in such buildings.