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Donald J. Trump’s march toward the Republican presidential nomination has sent shock waves through American politics and, as he continued gobbling up delegates this week, the rest of the world has started quivering, too.

From China and Russia to Europe and Australia, Mr. Trump’s ascent is being watched with increasing wariness. Could an angry reality television star really win the White House? Are street fights and name-calling what democracy has come to?

The Chinese government tends to avoid meddling in the political affairs of other countries, but this week its state-run media could not resist weighing in on Mr. Trump. An editorial in the English language Global Times pointed to the fisticuffs at his canceled rally in Chicago last Friday as evidence that democracy is a flawed system and said that Mr. Trump’s language is “abusively racist and extremist.”

“Fistfights among voters who have different political orientations is quite common in developing countries during election seasons,” it said. “Now, a similar show is shockingly staged in the U.S., which boasts one of the most developed and mature democratic election systems.”

Russia has been one of the few countries where Mr. Trump has been praised since embarking on his campaign, thanks to his flattery of President Vladimir V. Putin as a strong leader. But Mr. Putin’s camp was not amused on Thursday after Mr. Trump released an online video that featured him throwing someone to the mat in a judo competition to make the case that Hillary Clinton was not tough enough to handle the Russian strongman.

“The demonization of Russia and everything connected to Russia is, unfortunately, an obligatory part of an American election campaign,” Dmitry Peskov, Mr. Putin’s spokesman, said of the video. “We regard it negatively.”

Mr. Trump’s string of primary victories on Tuesday has also been cause for concern in Europe. The British-based Economist Intelligence Unit, a prominent risk analysis firm, decided this week that it could no longer ignore the threat that a Trump presidency would pose to the world economy. Noting his protectionist positions on trade and his muddled Middle East policies, the group said Mr. Trump was as dangerous as Jihadi terrorists are when it comes to being a drag on global growth.

“The impact for the world would be bad,” said Robert Powell, an analyst with the unit who worked on the study. “The impact for the U.S. would be even worse.”

Der Spiegel, the German newspaper, has also been dumbfounded by Mr. Trump’s rise. In an essay this week, Holger Stark, its Washington bureau chief, called out America’s press as culpable for the momentum behind his candidacy.

“Many newsrooms didn’t fulfill their democratic duty to monitor Trump, and to perform checks and balances, letting him get away with insults, lies and far-fetched promises,” Mr. Stark wrote in an essay. “When it comes to Trump, the critical public sphere has shown itself to be dysfunctional far too often in the last few months.”

In Australia, a haunting image of Mr. Trump hovering over Mount Rushmore sat next to a headline in The Daily Telegraph on Thursday. Anxious experts warned that his presidency would be “a disaster” for the country.

“The words ‘President Trump’ should give Australians pause,” Michael Fullilove, director of the Lowy Institute for International Policy, told the newspaper. “Mr. Trump reflects few of the values that have made America great. And judging from his speeches, he fails to see the advantages that flow to his country from being at the center of the global liberal order.”

The harshest response to Mr. Trump has come from Mexico, where two of its former presidents and its sitting president, Enrique Peña Nieto, have condemned his remarks about Hispanics as hateful and vowed never to finance the Trump-promised wall along the border. Mr. Nieto said last week that the Republican presidential candidate’s language was reminiscent of Hitler and Mussolini.

America’s northern neighbor has taken a more tempered approach. Prime Minister Justin Trudeau of Canada was peppered with questions about Mr. Trump during last week’s state visit to the United States, but he insisted that he did not intend to “pick a fight” with someone he may need to work with.

“I have faith in what Lincoln referred to as ‘the better angels of American nature,'” Mr. Trudeau said diplomatically in an interview with CBC. “I am looking forward to who I am going to work with after Nov. 4.”