Taiwan said on Saturday it supported the efforts of the Vatican to reach out to Beijing and hoped the move would improve China's "deteriorating religious freedom and human rights issue."
Pope Francis is currently in Mongolia on a state visit. As his papal plane passed over China's airspace, the pontiff sent a customary telegram to Chinese President Xi Jinping bearing "greetings of good wishes."
The Holy See is Taipei's only diplomatic ally in Europe and does not have official ties with Beijing, which views self-ruled Taiwan as its own territory to be seized one day, by force if necessary.
"Our country fully respects religious freedom and supports the Holy See's continuous attempts to engage in dialogue with China to resolve the Catholic Church's religious issues in China," Taiwan's Foreign Ministry said in a statement.
"We hope that Vatican-China exchanges will help improve China's deteriorating religious freedom and human rights issues and realize the ideal of religious liberalization in China."
The pontiff has led a years-long effort to build ties with Beijing and in 2018 the Holy See reached a secretive agreement allowing both sides a say in appointing bishops in China. The accord was renewed for two years in October.
In response to the pope's telegram, Beijing said it was keen to "strengthen mutual trust" with the Vatican and that the pope's words "reflect friendship and goodwill."
Customary telegrams were sent to China and nine other countries as the pope flew through their airspace.
The visit to Mongolia -- Francis' 43rd voyage in his decade as head of the Catholic Church -- is also crucial in keeping the door open for improved Vatican ties with Beijing.
But better relations with China could spell trouble for Taiwan, which has seen nine diplomatic allies poached by Beijing since Taiwanese President Tsai Ing-wen came to power in 2016.
Beijing reviles Tsai for not accepting the view that Taiwan belongs to China, and detests any diplomatic overtures made by countries that appear to treat the island like a sovereign nation.
Only 13 countries across the world officially recognize Taipei over Beijing.