* China denies "arbitrarily" sentencing Canadian to death
* Canadian's lawyer says will appeal, says evidence insufficient
* Canada formally asks for clemency for condemned man
* U.N. says death penalty should only be for intentional murder (Adds Canada asking for clemency for condemned man, foreign minister stressing close ties with China)
By Michael Martina, Philip Wen and David Ljunggren
BEIJING/OTTAWA, Jan 15 (Reuters) - China denounced Canada on Tuesday for "irresponsible" remarks after Canadian Prime Minister Justin Trudeau accused it of "arbitrarily" sentencing a Canadian to death for drug smuggling, aggravating already icy relations.
Hours later, in an apparent bid to ease tension, Canadian Foreign Minister Chrystia Freeland spoke of the "very important and long-standing ties" between the two nations.
The countries have been at odds since early December, when Canadian police arrested Meng Wanzhou, chief financial officer of Huawei Technologies Co Ltd, on a U.S. extradition request as part of an investigation into suspected violations of U.S. trade sanctions.
Days later, China detained two Canadians on suspicion of endangering state security.
Monday's death sentence for Canadian Robert Schellenberg for smuggling 222 kg of methamphetamines became the latest strain on ties.
Freeland said Ottawa had formally applied for clemency for Schellenberg, as it usually does in the cases of citizens condemned to death abroad.
"It's normal to have problems but we should also remember that the links between our two countries are very big," she told a televised news conference in Saint-Hyacinthe, Quebec, adding Canada had been in touch with Beijing at a number of levels.
"It is true that this is a difficult moment ... The best thing for both Canada and China, and frankly for the whole world, is to get past these current difficulties."
Freeland's office did not respond when asked whether she had been trying to defuse tensions with Beijing.
China has not linked any of the three Canadians' cases to Meng's arrest but has warned of severe consequences if she was not immediately released.
Trudeau said it should be of "extreme concern" to Canada's allies, as it was to his government, that China had chosen to "arbitrarily apply" the death penalty.
Chinese Foreign Ministry spokeswoman Hua Chunying expressed "strong dissatisfaction" with that.
"The remarks by the relevant Canadian person lack the most basic awareness of the legal system," Hua told reporters.
Taking Canada to task for issuing an updated travel advisory warning citizens about the risk of arbitrary enforcement of laws in China, Hua said Canada should instead remind its people to avoid drug smuggling.
"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.
The ministry later issued its own travel warning, citing the "arbitrary detention" of a Chinese national in Canada.
Schellenberg had appealed against an original 15-year prison sentence issued in November, but the court in Liaoning province sided with prosecutors at the retrial that the punishment was too light.
A lawyer for Schellenberg, Zhang Dongshuo, said his client would appeal.
Freeland said she had spoken to Schellenberg's father on Monday, adding it had been "a very emotional conversation for him". She gave no details.
Zhang said there was insufficient evidence to prove Schellenberg was part of a drug syndicate, or that he was involved in smuggling methamphetamines.
Even if the court accepted all the charges, it should not have increased his sentence, given that facts the prosecution gave as new evidence had already been heard, he told Reuters.
"Chinese law stipulates that during an appeal, only if new evidence is discovered and retried can there be an increase in the severity of a sentence," Zhang said.
Schellenberg was arrested in 2014.
Asked about the case, the United Nations noted its opposition to the death penalty apart from exceptional circumstances.
"The bottom line is that the death penalty shouldn't be imposed for any crime other than intentional killing," said U.N. human rights spokesman Rupert Colville.
Asked whether it had concerns about due process, he said: "In China there is generally a problem of lack of transparency in trials."
Chinese state media has played up coverage of Schellenberg's case following the deterioration in relations with Canada.
Drug smuggling is punished severely in China, and foreigners convicted of drug crimes have been executed before, including a Briton in 2009.
Schellenberg had faced a number of charges in Canada related to drug possession and trafficking, according to court records. But international rights groups condemned Schellenberg's sentence, with some saying it was too severe and may have been politically motivated. (Additional reporting by Julie Gordon in Vancouver, Christian Shepherd in Beijing and Stephanie Nebehay in Geneva; Editing by Nick Macfie, Andrew Cawthorne and James Dalgleish)