Texas Sen Ted Cruz and Gov Greg Abbott met with Ms Tsai on Sunday while she was passing through Houston on her way to visit Taiwan's Central American allies.
At a news briefing in Beijing on Monday, Foreign Ministry spokesman Lu Kang said China was firmly opposed to any contact between Taiwan's leader and "anyone from the US government".
He said such contacts threaten to disturb and undermine relations between Washington and Beijing.
China claims Taiwan as its own territory and has been ratcheting up diplomatic pressure on the independence-leaning Ms Tsai since her election last year.
Mr Cruz said in a statement that he and Ms Tsai "discussed our mutual opportunity to upgrade the stature of our bilateral relations" in their meeting, which addressed arms sales, diplomatic exchanges and economic ties.
An official with Republican President elect-Donald Trump's transition team said neither Mr Trump nor transition officials would meet with Ms Tsai.
Her stop in the US was scrutinised by Beijing for any signs that Mr Trump's team would risk its anger by further engaging with Taiwan.
President-elect Trump breached diplomatic protocol last month by speaking on the phone with the Taiwanese leader.
Mr Trump raised further concerns in Beijing when he questioned a US policy that since 1979 has recognised Beijing as China's government and maintains only unofficial relations with Taiwan.
US politicians often meet with Taiwanese presidents when they travel through the United States, most recently in June when Ms Tsai met in Miami with Republican Sen Marco Rubio of Florida.
The tabloid Global Times, published by China's Communist Party, said in an editorial on Sunday that Beijing would take a hard line toward any contacts between Taiwan's government and the incoming Trump administration. China "should also impose military pressure on Taiwan and push it to the edge of being reunified by force", it said.
China has "seized the initiative. The US and Taiwan now should restrain, or be forced to restrain, themselves", the newspaper said.
"Tsai needs to face the consequences for every provocative step she takes," it said.
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