Acting Foreign Minister Simon Birmingham said on ABC Radio on Wednesday the Australian government was "deeply concerned with this case".
"We urge the Canadian side to respect the rule of law, respect China's legal sovereignty, correct its mistakes, and stop making irresponsible remarks", Hua said.
Asked about Australia's support of Canada's position, Hua said she found it "rather odd" because Schellenberg was convicted of helping people who were planning to move methamphetamine from China to Australia.
"[Freeland and Pompeo] noted their continued commitment to Canada's conduct of a fair, unbiased, and transparent legal proceeding and United States extradition request with respect to Ms Meng Wanzhou, the Chief Financial Officer of Huawei", Palladino said.
Last week, Trudeau accused China of "arbitrarily and unfairly" detaining former diplomat Michael Kovrig and business consultant Michael Spavor, who were rounded up nine days after Canada arrested Meng.
Hua's comments are the latest sign of a sharply chilly turn in China-Canada relations since Canada detained a top Chinese telecommunications executive on December 1 at the request of the United States.
On Monday, Schellenberg was sentenced to death, causing Canada to issue its travel advisory and Prime Minister Justin Trudeau to express his government's "extreme concern" over how China had chosen to "arbitrarily apply" the death penalty to a Canadian citizen.
Chinese state television said in an earlier report that Schellenberg argued in court that he was a tourist visiting China and was framed by criminals.
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He was initially sentenced to 15 years in prison, which Schellenberg appealed last month.
Citing the Chinese constitution, ministry spokeswoman Hua Chunying told reporters on Wednesday that the court and procuratorate "exercise independent judicial authority and prosecutorial power according to the law and will not be interfered with by other administrative organs".
Chinese state media has played up coverage of Schellenberg's case following the deterioration in relations with Canada.
"We have very clearly outlined the case's facts and its seriousness", she told reporters.
Despite being sentenced to death, Mr Zhang said Schellenberg appeared "very peaceful and confident" about appealing the death sentence when they met on Tuesday.
But global rights groups condemned Schellenberg's sentence, with some saying it was too severe and may have been politically motivated.
Schellenberg was sentenced to death Monday, following a second trial in China for being an accessory to drug smuggling.
"The sudden retrial and apparent rush to judgment has highlighted the numerous flaws in China's judicial system, " China researcher William Nee said in a statement.
Asked if Beijing would consider the clemency request, the foreign ministry said China is a rule of law country. Freeland thanked countries and organizations _ Germany, France, the Netherlands, the European Union, the United States, Britain, Australia, Estonia, Lithuania and Latvia _ for "publicly coming out and speaking against these arbitrary detentions".