Cruz and Abbot met with 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 U.S. 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 Tsai since her election last year.
Cruz said in a statement that he and 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 Trump nor transition officials would meet with Tsai. Her stop in the U.S. was scrutinized by Beijing for any signs that Trump's team would risk its ire by further engaging with Taiwan, which China considers to be its territory.
Trump breached diplomatic protocol last month by speaking by phone with the Taiwanese leader. Trump raised further concerns in Beijing when he questioned a U.S. policy that since 1979 has recognized Beijing as China's government and maintains only unofficial relations with Taiwan.
U.S. lawmakers often meet with Taiwanese presidents when they transit through the U.S., most recently in June, when 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 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 U.S. 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.