"The Shanghai blast was caused by inflammables such as oil," Cheng Jiulong, the Shanghai municipal deputy head, said.
"The blast was indeed deliberate but had nothing to do with terrorist attacks."
A Yunnan provincial department of public security spokesman, said: "We have noticed media reports about the claims, but so far, no evidence has been found to indicate the explosions were connected with terrorists and their attacks, or with the Beijing Olympics."
IntelCenter, a US-based terrorism monitoring firm, said TIP had released a video entitled "Our Blessed Jihad in Yunnan", featuring a statement by commander Seyfullah, the group's purported leader, threatening next month's Olympic Games.
"Despite the Turkistan Islamic Party's repeated warnings to China and the international community about stopping the 29th Olympics in Beijing, the Chinese have haughtily ignored our warnings," IntelCenter quoted Seyfullah as saying.
The Islamic group warned there would be more attacks on the Beijing Games.
"Our aim is to target the most critical points related to the Olympics. We will try to attack Chinese central cities severely using the tactics that have never been employed," Seyfullah said, according to the IntelCenter transcript.
Shanghai police said on Thursday they had broken up an international terrorist group that had planned to attack an Olympic football preliminary match in the city, but gave no details about the group or the alleged attack.
Chinese officials have said their main Games security worries focus on separatist fighters seeking an independent Uighur homeland in the country's far west Xinjiang region and campaigners for an independent Tibet.
Turkistan is another name for the region the Chinese call Xinjiang. Its population comprises largely of Muslim Uighurs, who have a Turkic language and culture.