Mr Bush was sent by US President Bill Clinton to express concern over President Lee's remarks. Meanwhile US Assistant Secretary of State Stanley Roth has gone to hold talks on the issue in Beijing. However, President Lee stood by his controversial remarks, made two weeks ago. Senior Taiwanese government officials say they reject the mainland's concept of a One China and want to redefine the island's de facto status as a separate state. But he said Taiwan was still focused on the long-term goal of reunification.
China accuses Taiwan of a serious provocation and says it is trying to split the country.
And the country's state media has launched a new round of attacks, describing President Lee as an advocate of Taiwanese independence. Beijing has repeatedly threatened force if Taiwan took steps towards independence. Taiwanese officials say they have no evidence to confirm reports in Hong Kong newspapers that the mainland is now making military preparations close to the Taiwan Straits. They said Taiwan has not increased its own level of military alert. The BBC is not responsible for the content of external internet sites.