Mr Lee also told a cheering crowd at the stadium at Taoyuan, outside Taipei, that "pragmatic diplomacy" would secure Taiwanese people "the respect and treatment they deserve in the international arena", an unwelcome signal to Peking that the democratically elected president will proceed with Taiwan's drive for greater global status.
In Taipei, the stock market tumbled 4 per cent because of concern about China's reaction. The business sector was disappointed that Mr Lee had not mentioned moves towards direct air, shipping, and communications links with the mainland. After elections in March, which Mr Lee won by a landslide, there was speculation that movement on the "three links" might be one of Taipei's concessions.
The run-up to Taiwan's first democratic presidential elections was dominated by weeks of military manoeuvres by the People's Liberation Army (PLA) in and near the Taiwan Strait, as Peking tried to frighten voters away from supporting Mr Lee. Peking's fury against Mr Lee was ignited almost a year ago, when he secured a visa to visit the United States, prompting accusations from China that he was moving towards Taiwan independence.
Yesterday's speech trod a careful path between appearing to offer an olive branch while not actually offering anything that is likely to placate Peking.
"I would like to embark upon a journey of peace to mainland China, taking with me the consensus and will of the 21.3 million [Taiwanese] people," Mr Lee said. He was willing to meet top Chinese Communists "for a direct exchange of views in order to open up a new era of communication and co- operation between the two sides". Taiwan's independence was "totally unnecessary or impossible", he added.
The idea of a meeting between Mr Lee and his Chinese counterpart, Jiang Zemin, has been floated before, but has floundered on the question of the capacity in which Mr Lee would be received.
He would not be acceptable as President of Taiwan, or in any Republic of China governmental role, while Mr Lee would not tolerate being styled the mere head of a Chinese province.
It is unlikely a meeting would be considered until the two leaders had something concrete to discuss. The existing process of meetings, conducted only by supposedly non-governmental bodies, was halted by Peking last year after Mr Lee's success with the US visa.
By last night there was no official Chinese response to Mr Lee's speech. Peking will probably demand "concrete actions" from before relations improve. There are no plans, however, for any high-profile foreign trips, because Washington has lent on him to avoid actions which will again enrage Peking.
Some of Mr Lee's comments may annoy China's leaders. His slogan "Manage the great Taiwan, nurture a new Chinese culture", laid claim to a role as a custodian of Chinese culture.