Donald Trump’s administration is mired in scandal, senior Republican senator John McCain has said, but he urged America’s allies to stand by the nation as it navigates “troubled times”.

In a speech in Sydney, Australia, McCain said the US remained the most important country on Earth, and the global defender of “truth over falsehood”.

McCain also used the speech to launch a swingeing attack on China, accusing the emerging superpower of bullying other countries, stealing intellectual property and making illegal territorial claims in the South China Sea.

McCain, the decorated war veteran, senior senator from Arizona and former Republican presidential candidate, said many of America’s allies were fairly questioning the direction and reliability of Trump’s administration.

“My friends, I know that many of you will have a lot of questions about where America is headed under President Trump. Frankly, so do many Americans. What I would say is that the new administration is just that – new. It is still finding its feet.”

McCain conceded America’s reputation had suffered in the early months of Trump’s presidency as scandals over ties to Russia, alleged obstruction of an FBI investigation, nepotism and foundering relations with other world leaders rocked the administration with crippling regularity.

“We are going through a rough period,” McCain said. “We really are, and for me to tell you that we aren’t, politically, is not fair. But we’ve gone through other troubled times. I can remember the Watergate scandal and how it brought down a president. I’m not suggesting that’s going to happen to this president, but we are in a scandal and every few days another shoe drops from this centipede, and we’ve got to get through that.”

McCain said observers of the US must look beyond the president. “Our foreign friends always tend to focus on the person in the White House. But America is far bigger than that. America is our courts of justice. America is our state and local governments. America is our Congress.

“I know that the pushing and shoving and checking and balancing of my country’s institutions may not be pretty, but this vast intricate and beautiful system called American democracy is doing exactly what it’s supposed to do.”

In Australia as a guest of the United States Studies Centre at the University of Sydney, McCain said while he respected China’s economic and strategic rise, the country must conform to established global rules. “The challenge is that as China as grown wealthier and stronger, it seems to be acting more and more like a bully,” he said.

“It is refusing to open more of its economy so that foreign businesses can compete fairly. It’s stealing other people’s intellectual property. It’s asserting vast territorial claims that have no basis in international law and it’s using its trade and investment as tools to coerce its neighbours. The idea that China is now the steward of the open rules-based global economic order – it may sell at Davos – but people in this country, in this region, know better.”

McCain said China’s claims to territory and exclusive maritime rights within the so-called “nine-dash line” in the South China Sea were illegal and must be resisted. He said America, Australia, and other allies should work together in the region, including by exercising freedom of navigation in the area, to push back against Chinese island-building and militarisation in the sea.

McCain concluded his address with a plea to Australia and other US allies to “stick with us”. He said: “We need your help, my friends. Now more than ever.

“I realise that some of President Trump’s actions and statements have unsettled America’s friends. They have unsettled many Americans as well. There is a real debate under way now in my country about what kind of role America should play in the world and, frankly ... the future of the world will turn on a large extent on how this debate in America is resolved.”