HBO has agreed to extend John Oliver’s run on its satirical Sunday-night program “Last Week Tonight” through 2017, a move that puts to rest speculation that the British comic might be in line to succeed Jon Stewart at Comedy Central’s “The Daily Show,” where Oliver first won greater recognition.

“We are incredibly proud to have John as part of the HBO family,” said Michael Lombardo, president of programming at HBO, in a prepared statement. “His unique ability to deliver socially significant commentary week after week, along with his innate comedic brilliance, puts John in a class by himself.”

Oliver’s program has developed into a critical success since it launched in April. While ostensibly a satire of news programming, the show has delved into such topics as net neutrality, native advertising and, more recently, tobacco companies’ legal actions against small, poor countries in Africa and South America. Some of the segments are longer than those prepared for CBS’ venerable “60 Minutes” newsmagazine.

Oliver came to HBO after a successful stint on Comedy Central’s “Daily Show,” where he served as a correspondent starting in 2006. When Stewart took a break in 2013 to direct a movie, Oliver filled in for him, and the attention he garnered during that time made him a hotter commodity. Within three months of filling in for Stewart, he signed a deal with HBO.

That has not dampened chatter in recent weeks that Oliver would make a good successor for Stewart, who announced last week that he would leave Comedy Central’s flagship program later this year.

HBO said a third and fourth season of “Last Week Tonight” would each consist of 35 episodes, the same number Oliver is producing for the show’s current, second season.

“Last Week Tonight” is produced for HBO by Avalon Television. Executive producers are John Oliver, Tim Carvell, Jon Thoday, and James Taylor. Liz Stanton is co-executive producer. Diane Fitzgerald is producer. Jim Hoskinson is the director.