Lin Ti-chuan, 33, and her boyfriend were kidnapped in a row over money he allegedly owed to his mainland business associates. She died after being overdosed with sedatives.
A senior mainland official, Liu Gangqi, said the murder was an "isolated criminal case and should not have a negative effect on cross-Strait ties". However, the potential for political fallout is considerable. Taiwan's Vice-Prime Minister, Liu Chao-hsuan, has warned China that mishandling of the case could outrage the Taiwanese and harm efforts to improve relations.
Taiwan is already angry that a representative of its semi-official Straits Exchange Foundation was not allowed into the mainland to accompany the grieving relatives.
Last night discussions were still under way about whether there would be a post-mortem examination. Ms Lin's family do not want one, saying they want the body to remain "intact". Chinese officials say they will respect this decision, but are keen to obtain evidence for use in any trial.
The murder cut short a visit to Taiwan by Li Yafei, the deputy secretary- general of the Association for Relations Across the Taiwan Strait (Arats), who was the most senior mainland visitor for more than three years.
Relations between the two sides have thawed recently, with the announcement that later this year should see the resumption of direct talks between the heads of SEF and Arats, their first meeting since 1993.
Ms Lin was a city councillor in Kaohsiung and a member of the Democratic Progressive Party, the pro-independence Taiwanese opposition party. A week ago, she travelled to Dalian in the north-east Chinese province of Liaoning with her boyfriend, Wei Tian-kang, a businessman whose mainland associates said he owed them US$700,000 (pounds 43,000) on a deal.
Both Ms Lin and Mr Wei were kidnapped on arrival by three men and heavily sedated. A ransom of $200,000 was demanded.
Mr Wei managed to escape and go to the police when the kidnappers took Ms Lin to a hospital in Haicheng after she slipped into a coma. Her body was discovered in the hospital mortuary on Friday. Doctors said she was dead on arrival.
The mainland company said to be involved with Mr Wei was Huamei Industry, which supplied magnesium. One of the suspects is a Liaoning boss at the company.
On the mainland, Mr Liu said those connected with Ms Lin's death "will be arrested and punished promptly", but he criticised "some people in Taiwan" for making political capital out of her death.
The DPP, which had only recently lifted a ban on mainland contact and was working to build a relationship with Peking, said it would suspend all interactions with China.
Chang Chun-hong, a party MP, said: "We will mobilise our legislature to boycott all Taiwan's cultural, sports and social exchanges with the mainland."
The party's secretary-general, Chiu Yi-jen, said the murder was "by no means an isolated incident." In 1994, 24 Taiwanese tourists were robbed and burnt to death on a boat at Qiandao Lake, Zhejiang province.Reuse content