Troops and tanks forcibly cleared peaceful protesters from Beijing's Tiananmen Square on June 4, 1989, after weeks-long demonstrations demanding greater political freedoms.
The exact toll is unknown but hundreds died, with some estimates exceeding 1,000.
China's communist rulers have since sought to erase any public mention of the crackdown, with censors scrubbing all online references.
Police were seen by AFP on Wednesday at the entrance to Wan'an Cemetery, a site in west Beijing where victims of the crackdown are known to be buried.
Officers were also posted at several intersections leading into Tiananmen Square.
On Wednesday evening, a line of buses and a cherry picker partially blocked screens at the German and Canadian embassies showing images of candles, a symbol commonly used to pay tribute to Tiananmen victims.
- 'Never forget' -
Rubio said in a statement the "world will never forget" what happened in Tiananmen Square, even as Beijing "actively tries to censor the facts".
"Today we commemorate the bravery of the Chinese people who were killed as they tried to exercise their fundamental freedoms, as well as those who continue to suffer persecution as they seek accountability and justice for the events of June 4, 1989," Rubio said.
Chinese foreign ministry spokesman Lin Jian hit back during a briefing in the capital, saying Beijing had "lodged a solemn protest" over the top diplomat's comments which "maliciously distort historical facts... and seriously interfere in China's internal affairs".
Taiwanese President Lai Ching-te echoed Rubio's remarks, vowing to preserve the memory of victims of the bloody crackdown.
"Authoritarian governments often choose to be silent and forget history; democratic societies choose to preserve the truth and refuse to forget those who have contributed to the ideal of human rights and their dreams," Lai said on Facebook.
China claims Taiwan is part of its territory and has threatened to seize the democratically-run island by force.
- 'Reaffirm our commitment' -
In Hong Kong, jailed activist Chow Hang-tung began a 36-hour hunger strike Wednesday, a dogged attempt to individually commemorate the anniversary in a city that once hosted huge public remembrances.
The former lawyer used to help organise an annual vigil that drew tens of thousands to Victoria Park.
Hong Kong had been the only place under Chinese rule where commemoration of the crackdown was tolerated.
Slogans at the candlelight vigil sometimes called for democracy in China and an end to one-party rule.
But after huge and sometimes violent protests roiled the city in 2019, Beijing brought in a wide-ranging national security law that has quashed political dissent.
The public memorial has effectively been banned and Chow imprisoned, facing a potential life sentence on subversion charges.
On Wednesday, AFP journalists saw at least seven people taken away by police around Victoria Park, including two schoolgirls holding white flowers -- which often signify mourning in Chinese culture -- and a man standing in silent tribute.
Some people were stopped and searched.
Hong Kong police said 10 people were detained and suspected of "breach of the peace." Seven of them were released soon thereafter.
It was not clear if the seven seen by AFP being taken away were among those reported arrested.
"It's a shame that there's no more (vigils)... In fact, no one will ever forget," a man named Yuen, 49, who did not give his first name, told AFP.
Over the last few years, activists have been detained for "offences in connection with seditious intention" around the anniversary.
In a social media post, Chow said her hunger strike would "commemorate this day and reaffirm our commitment" and urged authorities to apologise over her "wrongful" imprisonment.
"History tells us that (the apology) will likely take a very long time -- the Tiananmen Mothers have been waiting for 36 years and still have not received an apology," she said, referring to an activist group made up of families of victims of the crackdown.
A video featuring 87-year-old Zhang Xianling, whose 19-year-old son was killed in 1989, circulated online last week.
"The lights in Victoria Park may have been blown out by the gales, but the sparks of justice will glow in the hearts of every conscientious person," she added.
At a vigil Wednesday on Taipei's Liberty Square, 20-year-old American student Lara Waldron told AFP: "I feel like this June 4 is very close to me right now.
"As a college student, I'm of the age of many organisers and participants -- people (who) lost their lives in Tiananmen."
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