Albania is processing the request from the ethnic Uighurs, who arrived on Friday. The United States, which held them in Guantanamo for almost four years without charge or trial, said it would not hand them back to China because they might face persecution there.
Tian Changchun, the Chinese ambassador, said in a statement: "We have contacted the Albanian side and want them to repatriate to China the five terrorists holding Chinese citizenship as soon as possible.
"In accordance with international law, the defendants should return to China."
The Chinese ambassador said the Eastern Turkistan terrorist organisation had ties to al-Qaeda, had backed the Taliban in Afghanistan and had been named in a United Nations list of terrorist groups.
Ethnic Uighurs come from Xinjiang province in western China. Many Muslim Uighurs seek greater autonomy and some want independence from China. Beijing has waged a campaign against what it calls the violent separatist activities of the Uighurs.
Diplomatic sources said the US asked more than 20 countries to take in the men before asking Albania, the only country to accept.