Cablevision Systems Corp. Chief Executive James Dolan assured investors that a “landslide” of cord-cutting likely won’t happen in the near-term, though he projected declines over the next several years.

“I don’t think the sky is falling quite yet,” Mr. Dolan said, in response to questions during Cablevision’s second-quarter earnings conference call about the bleeding of media and cable stocks this week. Cablevision shares, which had been buoyed by deal speculation as suitors have expressed interest, fell 2.7% Friday to $25.82 after falling 5% over the last two days.

Mr. Dolan said it would take at least five years for there to be a 10% decline in the U.S. pay-TV customer base and 10 years before 30% have dropped their subscriptions. That is in part because online video options today don’t have the “programming weight” the traditional television bundle has, Mr. Dolan said.

Cablevision executives also noted that new “cord-cutter” packages the company has been offering—including fast broadband, a digital antenna to pick up broadcast signals, and Internet-delivered HBO—are attracting new customers, but they aren’t leading existing customers to downgrade.

Mr. Dolan said that “eventually” the content on Web TV platforms will become more robust and competitive with the big bundle. And as cable bills rise due to ever-increasing programming carriage costs, “that will drive people who are more price-sensitive into alternatives, and the Internet is obviously starting to become a real alternative,” he said.