Similarly, Colorado Republican Sen. Cory Gardner, chairman of the Senate Foreign Relations subcommittee on East Asia and Pacific affairs, said he looks forward to working with the president-elect to find ways to "strengthen our relationship with our ally and friend, Taiwan.”
“The friendship between our two countries is important, and I am glad to hear the president-elect is committed to that friendship," Gardner said in a statement.
"I commend President-elect Trump for his conversation with President Tsai Ing-wen, which reaffirms our commitment to the only democracy on Chinese soil,” Cotton said. “I have met with President Tsai twice and I'm confident she expressed to the president-elect the same desire for closer relations with the United States."
Taiwan has held that it is an independent nation since it split from the Chinese mainland in a 1949 civil war.
But the U.S. has maintained a "one China" policy since establishing diplomatic relations with Beijing in 1979, meaning that it has not recognized Taiwan as its own country, but rather as a part of China. Since then, there have been no publicly reported phone calls between a U.S. president or president-elect and a Taiwanese leader.
The U.S. does have a "robust unofficial relationship" with Taiwan and commits to defending it in the event of a Chinese attack, according to the Department of State's website.
The White House did not know about the call until after it took place.
And since news of the call broke, some Capitol Hill Democrats have expressed bewilderment at Trump’s sudden departure from years of established policy.
Hawaii Democratic Sen. Brian Schatz took to Twitter to appeal for clarification and to call for a “steady hand” from Trump’s yet-to-be-named secretary of state.
China meanwhile has lodged a formal diplomatic protest, what a spokesman called "solemn representations" to the U.S., over Trump's phone call.
"There is only one China in the world, and Taiwan is an inseparable part of Chinese territory,” Chinese foreign ministry spokesman Geng Shuang told reporters in Beijing. “The government of the People's Republic of China is the sole legitimate government representing China. This is a fact that is generally recognized by the international community."
He said China urged the relevant parties in the United States to handle Taiwan-related issues "cautiously and properly" to avoid "unnecessary interference" in the China-U.S. relationship. He did not describe details of China's complaint to the U.S., or say with whom it was lodged.