CANBERRA, Aug 11 (Reuters) - Australia told China to rein-in its diplomats on Tuesday, after Beijing's Canberra embassy tried to block a speech by an exiled Uighur leader, adding to strained relations over China's spy allegations against Rio Tinto.

The embassy's Political Counsellor Liu Jing met management at Canberra's National Press Club last week and requested they withdraw an invitation to Rebiya Kadeer to speak on Tuesday, the club said.

Kadeer is blamed by Beijing for instigating last month's ethnic riots in Xinjiang province.

"Embassies, diplomats, officials are entitled to put views in Australian society, but when they put those views, those views have to be put appropriately," Australia's Foreign Minister Stephen Smith told state radio.

"They can be put firmly, but they need to be put politely and appropriately," Smith said.

Kadeer's visit to Australia has been controversial since Chinese consulate officials in Melbourne last month protested over inclusion of a documentary about ethnic Uighurs in Australia's biggest film festival.

China's government accuses Kadeer's World Uighur Congress of being a front for extremist militants pushing for a separate East Turkistan homeland. She was arrested in 1999 and found guilty of "providing secret information to foreigners".

Liu told the press club it would be "regrettable" if diplomatic relations between Australian and China were harmed by Kadeer speaking there, said club Chief Executive Maurice Reilly.

"The press club and the board have a long-standing policy of 40 years or more that they decide who speaks at the press club, and they are quite free of outside influence," said Reilly, confirming Liu's approach.

"We listened respectfully and we pointed out that China has a different social system to our social system," Reilly said. The press club is Australia's top venue for political speakers, hosting international figures, heads of state, religious leaders and business leaders since 1963.

Smith said he had told Chinese diplomats that their vigorous opposition to public appearances by Kadeer in Australia was only increasing her public profile.

The pressure to cancel Kadeer's speech comes as relations between China and Australia are being tested in the wake of the arrest of senior Australian Rio Tinto (RIO.AX) executive Stern Hu on commercial espionage charges.

Smith said accusations in the online edition of a magazine published by China's state secrets agency this week that Rio Tinto spied on Chinese steel mills for six years, resulting in a $102 billion iron ore loss for China, were not official.

"It is now quite clear given that the article has been taken off the website that is was essentially the opinion of the individual writer, and not if you like officially sanctioned," he said. For full coverage of the iron ore probe, click [ID:nSP473911] and for more stories on ethnic unrest in China, click on [ID:nXINJIANG]) (Editing by James Thornhill)