Both Beijing and Washington have described Saturday's attack in Kunming which killed 29 people and injured 143 as terrorism. China blames separatists from its restive far-western region of Xinjiang, home to the mainly Muslim Uighur minority.
Qin Guangrong, the Communist Party chief of Yunnan province which includes Kunming, said the eight attackers travelled to his province and Guangdong, which borders Hong Kong, as they tried to leave the country, China Radio International said, in a report that was later deleted from its website.
"They couldn't get out at Yunnan so tried to get out in other places, but they also couldn't leave Guangdong, so once again they returned to Yunnan."
When the group failed to escape through southern Yunnan's Honghe county -- which borders Vietnam -- they hatched the plan to target either the frontier area or Kunming's transport terminals, the report quoted Qin as saying.
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His comments had some similarities with an earlier report by US-funded broadcaster Radio Free Asia (RFA), which quoted sources as saying the eight attackers travelled from Xinjiang to Yunnan in order to cross the border into Laos on their way to seek sanctuary elsewhere.
The sources said they could have given up their attempt to leave after another group of about 30 Uighurs was detained in the border area in September.