A group of New York politicians is lobbying Comcast to provide free broadband to all city public housing residents and expand other low-cost Internet offerings as a condition for the cable operator’s proposed $45 billion merger with Time Warner Cable.

Led by New York City’s public advocate, Letitia James, and City Councilman Ben Kallos, the group of state and local politicians is calling on Comcast to help bridge the so-called digital divide between people who have access to broadband connections and those who do not. About a third of New York City families do not have broadband, according to the Knight Foundation.

“With every second we wait, the digital divide is widening,” Mr. Kallos said. “What we have with the Internet is literally a portal to the world’s knowledge. One third of our city can’t get on the Internet and can’t learn whatever, whenever they want.”