Chinese state media has warned the US against deviating from the one-China policy, hours after the Taiwanese leader stopped briefly in Houston.
Tsai Ing-wen met Texas Senator Ted Cruz and Governor Greg Abbott during her stopover en route to Central America.
But a spokeswoman for President-elect Donald Trump said that neither he nor his team would meet Tsai.
China reacted angrily when Trump spoke to Tsai by telephone late last year, in a major break from the past.
No US president or president-elect had spoken directly to a Taiwanese leader for decades.