"Mr Hu made some admissions concerning some of those bribery amounts, so he did acknowledge the truth of some of those bribery amounts," Connor said.
Wang Yong, another executive on trial, pleaded guilty "in part" to accepting bribes, his lawyer Zhang Peihong said, but is contesting a $9m portion of the $10.25m he is charged with accepting.
It has not been made clear if Liu Caikui and Ge Minqiang have accepted any charges of bribery.
Rio Tinto has said the four men did nothing wrong.
While the trial was opening in Shanghai, Tom Albanese, Rio's chief executive, signalled to an audience in Beijing that he did not want to jeopardise business ties with China, the world's biggest consumer of iron ore.
"This issue is obviously of great concern to us," Albanese told a forum of officials and executives, referring to the case.
"I can only say we respectfully await the outcome of the Chinese legal process," he told the forum, held in an exclusive state guesthouse.
Albanese said "we remain committed to strengthening our relationship with China, not just because you are our biggest customer, but because we see long-term business advantages for both of us".
The Australian department of foreign affairs and trade released a statement over the weekend saying: "The Government's disappointment with the decision has been registered with Chinese officials in Beijing and Canberra."
Kevin Rudd, the Australian prime minister, told reporters on Monday that his government would be "monitoring the trial very carefully".
"China has a different legal system to Australia; China has a different legal system to the rest of the world," he said. "The world will be watching very closely."
The men face up to seven years in jail if convicted on charges of commercial espionage and five years or longer in jail if found guilty of bribery.
Mei Xinyu, a columnist in the Chinese-language Shanghai Securities News, said: "The Australian government and public need to calmly and rationally consider this question: should the government waste such a large amount of political and financial resources to pay the bill for certain companies' immature and even illegal ways?
Greg Sheridan, foreign editor of The Australian, tells Al Jazeera that the charges are 'political'
"What Rio Tinto and Stern Hu did would be utterly taboo in any host country," Mei, a ministry of commerce think tank researcher, said.
The four employees from Rio's iron ore team were detained last summer at the height of negotiations over 2009 ore prices, creating an uproar over China's state secrets laws.
Chinese media last summer accused the four of seeking information about Chinese mines and steel mills, which many firms consider legitimate market information.
Foreign reporters were not allowed to attend the trial.
China has excluded Australian diplomats from observing the part of the trial concerning commercial secrets, drawing protests from Canberra, which says they have the right to be present for the whole trial, scheduled to last three days.
The trial opened on the same day that internet giant Google may announce whether it will pull out of China over its complaints about censorship and hacking, reports have suggested.