In the first major fracture between television show owners and the wildly popular Hulu.com, Viacom will remove “The Daily Show With Jon Stewart,” “The Colbert Report” and other Comedy Central programs from the video site next week.

The companies said Tuesday evening that they were parting amicably, but Viacom’s decision is a serious loss for Hulu. This week “The Daily Show” is listed as the third-most-watched show on the site, behind “Lost” and “Family Guy.” The decision also highlights the large gulf between the expectations of consumers — who demand a wealth of free and easily accessible content on the Internet — and the media companies, who are seeking a more profitable business model online.

“We tried to reach a deal. We got close. We continued to talk even over the weekend. But we could not agree on a price,” said a person involved in the Viacom negotiations who requested anonymity because the process was conducted in private.

The three-year-old Hulu dominates the mushrooming market for online full-episode TV viewing, with more than 44 million monthly visitors, according to comScore, the online measurement firm. The site’s monthly video view totals have surged in recent months, from 580 million last September to 1.01 billion last December. But Hulu is unprofitable, according to analysts. The site’s advertising sales staff has struggled at times to keep pace with the torrid growth, and a partial pay model has been discussed by its owners, which include three of the broadcast networks, ABC, NBC and Fox.