China's foreign ministry spokesperson Hua Chunying has called on the Vatican - one of only 23 sovereign states in the world that recognise Taipei instead of Beijing - to sever diplomatic ties with the island.
The Vatican should "recognise the Chinese government as the sole legal representative of all China", the spokesperson said on Sunday.
She also said China hoped Francis would "take concrete steps to create conditions for the improvement of China-Vatican relations".
The last time a Taiwanese leader visited the Vatican was in 2005, when then president Chen Shui-bian attended the funeral of pope John Paul II.
An incensed Beijing refused to send a representative and filed a protest to Italy for issuing Chen a visa.
This time, it appears to be boycotting again but the Vatican has emphasised it has not sent out specific invitations.
"No one is privileged, no one is refused, everyone is welcome if they say they are coming," Vatican spokesperson Federico Lombardi said.
Li Xiaoyong, spokesperson for the Chinese embassy in Rome, said: "There will be no delegation from China. China has expressed its congratulations.
"We hope that with the guidance of the new pontiff, the Vatican side can take a step towards us for a dialogue with mutual respect," he said.
Bernardo Cervellera, director of AsiaNews in Rome, a Catholic news agency specialising in Asian affairs, said: "The Vatican cannot block Taiwan from coming. It is a public ceremony."
He said the Chinese reaction was "like a broken record - it masks the fact that they do not really know what to do".
"They are stuck in their own succession," he said, referring to the nomination last week of new President Xi Jinping.
China's communist regime broke ties with the Vatican in 1951 and six years later set up its own Catholic church, which does not recognise the pope as its head, while the Vatican continued to direct its own unofficial church in China.
Anthony E Clark, an expert on the faith in the country, who teaches Chinese history at Whitworth University in the United States, said: "China's official stance toward the Vatican is that the pope should have no governing role in China's Catholic community.
Relations worsened under Benedict XVI, with the Vatican excommunicating at least three bishops ordained by the official church in China and Chinese authorities curtailing the freedoms of prelates.
The dispute is reminiscent of historical disputes between the Vatican and the lay governments of Europe. The Vatican alone reserves the right to name bishops, while China sees this as a type of interference in its internal affairs.
Cervellera said the Argentine pope would be well equipped to deal with Asian affairs because of his experience of working under Argentina's authoritarian regime and his advocacy on poverty issues during an economic crisis there.
"Asians feel him very close," he said.
Cervellera said the Vatican had signalled it was willing to sever diplomatic ties with Taiwan and that the ball was in China's court.
Cardinal Joseph Zen Ze-kiun, the archbishop emeritus of Hong Kong, agreed.
"All the popes have been very understanding with Beijing. Now it is up to China's new leadership," he was quoted by Italian media as saying.
The dispute has left China's Catholics - a minority among the estimated 67 million Christians of all denominations - feeling vulnerable.
There are believed to be up to 12 million Catholics in China.
Bishop John Fang Xingyao, chairperson of the state-sanctioned Chinese Catholic Patriotic Association, was quoted by Hong Kong's South China Morning Post as saying he hoped the new pope would "turn over a new leaf" in relations.
"Given that God has chosen the new Pope as a leader, I'm sure he would grant him the ability to build better relations," Fang said.
In negotiating the difficult diplomatic waters, Francis could take inspiration from Matteo Ricci, a fellow Jesuit and a fluent Mandarin speaker who became a famous missionary in China at the end of the 16th century.
Ricci's book The True Meaning of the Lord of Heaven argued that Confucianism - the great Chinese philosophy - and Christianity were not opposed but in fact very similar.