* Exiled Uighur leader: China must understand Uighur issues to reduce tension
* Uighur group offers condolences to victims of knife attack
* Chinese foreign ministry denounces group's "ulterior motive" (Adds suspect confesses)
By Ben Blanchard
BEIJING, March 4 (Reuters) - A prominent exiled Uighur leader has urged China's government to respond calmly to a knife attack in the country's southwest and not "demonise" ethnic Uighurs after Beijing blamed the mass killings on extremists from the far western region of Xinjiang.
Rebiya Kadeer, President of the World Uyghur Congress, also said tension could only be reduced in Xinjiang if China acknowledged rights issues faced by the large Uighur minority.
China has vowed to crack down on what it says are militants bent on transforming Xinjiang into an independent state called East Turkestan. But it has also emphasised ethnic unity after what it called a terrorist attack on Saturday in Kunming in which 33 died, including four assailants.
Many Muslim Uighurs object to Chinese curbs on their culture and religion, though authorities say they enjoy broad freedoms.
"At this time of heightened tensions, it is important for China to deal with the incident rationally and not set about demonising the Uyghur people as state enemies," Kadeer said in the English-language statement, using the group's spelling for the Uighur minority.
"The fact remains that peaceful dissent against repressive government policies targeting Uyghurs is legitimate, so the Chinese government must not conflate this constructive criticism with the events of 1 March.
"It is absolutely vital the Chinese government deal with the longstanding and deteriorating human rights issues facing Uyghurs if tensions are to be reduced."
Kadeer is a former Chinese political prisoner accused of leaking state secrets in 1999 who left China on medical parole and settled near Washington with her husband and part of her family in 2005.
She previously had been a celebrated millionaire who had advised China's parliament, and is now condemned by Beijing as an "anti-Chinese splittist".
FOREIGN MINISTRY DENOUNCES GROUP
Chinese Foreign Ministry spokesman Qin Gang condemned both her group and her comments.
"The so-called World Uyghur Congress is an anti-China separatist group. They have no capacity to represent China's Uighur people," he told a daily news briefing.
"Her remarks make it obvious that she is seeking to take the serious violent terrorist incident in Kunming and link it to a certain ethnicity. This shows an ulterior political motive."
The group's statement added that the World Uyghur Congress "unequivocally condemns the violence that took place at Kunming railway station" and expressed condolences to victims' families.
The government has not explicitly accused Uighurs of carrying out the attack, though by calling them Xinjiang extremists the implication is clear.
The one person identified by Beijing as being an attacker, Abdurehim Kurban, appears to be Uighur, judging by his name.
Another of the suspected attackers, a woman, has regained consciousness in hospital and "confessed to (her) crimes", Yunnan's provincial Communist Party boss Qin Guangrong said, according to a website run by the state prosecutor's office.
In Kunming, capital of the southwestern province of Yunnan, many hundreds of kilometres (miles) from Xinjiang, members of the small Uighur community have said they felt under suspicion.
The government has responded with anger to suggestions its policies may be to blame for violence in Xinjiang, saying that it faces a real threat from "terrorists".
Fu Ying, spokeswoman for China's largely rubber-stamp parliament, which opens its annual session on Wednesday, told reporters that the Kunming attackers were "inhuman" killers and that the world should unite to combat terrorism. (Additional reporting by Megha Rajagopalan; Editing by Ron Popeski and Clarence Fernandez)