The media mogul Rupert Murdoch denounced an “awful woke orthodoxy” and declared, “I’m far from done,” while accepting a lifetime achievement award this weekend.

Mr. Murdoch, 89, made the remarks in a prerecorded video shown on Saturday during a virtual event for the United Kingdom nonprofit that honored him, the Australia Day Foundation. The video was shared on the website of The Herald Sun, a newspaper in Melbourne owned by Mr. Murdoch.

The video is noteworthy because Mr. Murdoch, despite exerting enormous influence over the global media landscape as the executive chairman of News Corp, has been relatively quiet publicly in recent years. He has been weathering the pandemic in his home in the Cotswolds in England, and received a Covid-19 vaccination in December.

In the video, Mr. Murdoch, standing next to a bottle of Australian red wine and wearing a medal, thanked the foundation for the award in the video but said his career “that began in a smoke-filled Adelaide newsroom is still in motion.”

He also took the opportunity to condemn “cancel culture.”

“For those of us in media,” he said, “there’s a real challenge to confront: a wave of censorship that seeks to silence conversation, to stifle debate, to ultimately stop individuals and societies from realizing their potential.”

He continued: “This rigidly enforced conformity, aided and abetted by so-called social media, is a straitjacket on sensibility. Too many people have fought too hard in too many places for freedom of speech to be suppressed by this awful woke orthodoxy.”

It seems Mr. Murdoch’s beliefs have been noted by the editors of his publications. On Monday, The New York Post published an op-ed by Senator Josh Hawley, Republican of Missouri, on the front page of the paper with the headline “Time to take a stand against the muzzling of America.”

Mr. Hawley, who has been widely condemned for his role in trying to overturn the result of the presidential election even after the Capitol riot on Jan. 6, echoed Mr. Murdoch in denouncing “woke orthodoxy.”

Mr. Hawley also used his front-page column in one of the most widely circulated newspapers in the country to bemoan the revoking of his book deal and the canceling of events he had scheduled. Mr. Hawley’s publisher, Simon & Schuster, dropped his book after the Jan. 6 siege, though it was quickly picked up by the conservative publishing house Regnery Publishing.

The New York Post declined to comment.

Mr. Murdoch’s media empire, which includes The Post and Fox News, is trying to navigate a tense political moment. It is attempting to maintain conservative viewers who, unhappy with some of the straight news reporting on Fox, tuned in to Newsmax and One America News, which embraced former President Donald J. Trump’s false claims about election fraud. Fox News executives this month fired the politics editor Chris Stirewalt, who was an on-screen face of the network’s election night projections, and introduced more right-wing opinion programming.