If the two countries move ahead, it could be a watershed moment for the era of global social media. No established democracies have ever come as close to applying such sweeping restrictions on online communication, and the demand for change has both harnessed and amplified rising global frustration with an industry that is still almost entirely shaped by American law and Silicon Valley’s libertarian norms.

“Big social media companies have a responsibility to take every possible action to ensure their technology products are not exploited by murderous terrorists,” Scott Morrison, Australia’s prime minister, said Saturday. “It should not just be a matter of just doing the right thing. It should be the law.”

The push for government intervention — with a bill to be introduced in Australia this week — reflects a surge of anger in countries more open to restrictions on speech than in the United States, and growing impatience with distant companies seen as more worried about their business models than local concerns.

There are precedents for the kinds of regulations under consideration. At one end of the spectrum is China, where the world’s most sophisticated system of internet censorship stifles almost all political debate along with hate speech and pornography — but without preventing the rise of homegrown tech companies making sizable profits.

No one in Australia or New Zealand is suggesting that should be the model. But the other end of the spectrum — the 24/7 bazaar of instant user-generated content — also looks increasingly unacceptable to people in this part of the world.