Mack Horton and Sun Yang continued their bitter feud at the world championships in Gwangju Tuesday, hours after the Australian was warned by FINA over his podium snub of the controversial Chinese swimmer.

The pair eyeballed each other as they closely passed on the pool deck during the morning's 800m freestyle heats, prompting Sun to glare back over his shoulder at Horton before waving to fans as he left the arena.

The pair swam in separate heats of the 800m free with Sun scraping through eighth fastest, but there will be no renewal of their row in Wednesday’s final because Horton failed to qualify.

Horton, who took silver behind Sun at the weekend, refused to step onto the top step of the podium for photos after the medal ceremony for Sunday's 400m free, as doping allegations swirl around China's multiple Olympic champion.

The Australian's protest reignited their row at the 2016 Rio Olympics, where Horton labelled Sun a "drug cheat" over a prior doping ban before pipping the Chinese giant to gold.

It also angered Sun, who accused Horton of "disrespecting China," and triggered a backlash on social media.

The Australian's Instagram account has been trolled by Chinese users, some even posting death threats against Horton and his family.

Australian team mate Jack McLoughlin condemned the threats after Tuesday's heats.

"They're pretty bad -— I wouldn't wish that on my worst enemy. It's just really bad for everyone, and swimming and sport in general. I think what he's standing for is right," he said.

A statement was issued late Monday from swimming's governing body warning Horton and Swimming Australia of their responsibilities to the sport.

"While FINA respects the principle of freedom of speech, it has to be conducted in the right context.

- 'Protect the team' -

"As in all major sports organisations, our athletes and their entourages are aware of their responsibilities to respect FINA regulations and not use FINA events to make personal statements or gestures," it added.

Horton chose his words carefully after his 800m heat. "As much as I want to protect the sport, I still need to protect the team," he said.

"The focus now is the team's performances and making sure we get through the week."

Swimming Australia backed Horton's stand. "Swimming Australia respects the position Mack Horton took during the medal ceremony and understands his sense of frustration," said CEO Leigh Russell.

Sun, who has always protested his innocence over the three-month suspension he served in 2014, is again competing under a doping cloud after a leaked FINA doping panel report alleged he smashed blood samples with a hammer after being visited by testers last year.

FINA cleared Sun to take part in the world championships, but the World Anti-Doping Agency has appealed that decision to the Court of Arbitration for Sport (CAS).

After the pair clashed in Rio, China's state-run media called Australia a "second-class citizen" of the West and accused it of "white supremacy".

The China Daily weighed on their latest run-in, saying Horton had "humiliated himself" with his protest.

"Needless to say such moves are rather rude and lack the most basic manners," it added in a commentary.

"Not joining Sun on the podium was not a protest, but an insult."