China on Friday slapped sanctions on two American organisations that hosted Taiwan's President Tsai Ing-wen during her visit to the US and her meeting with the House Speaker, a day after President Xi Jinping said it is "wishful thinking" to expect Beijing to "compromise" on its stand on the self-ruled island.

Ms Tsai's meeting with US House Speaker Kevin McCarthy - the third most senior official in the US - on Thursday took place against the backdrop of repeated warnings from Beijing to Washington that the meeting should not happen. It was the first time a Taiwan president had met a US Speaker on American soil.

China views any official exchanges between foreign governments and Taiwan as an infringement on Beijing's claims of sovereignty over the island.

China's Ministry of Foreign Affairs announced that the Washington-based think tank Hudson Institute and the Ronald Reagan Presidential Library in California would be banned from any cooperation, exchange or transaction with institutions and individuals in China.

The Ronald Reagan Presidential Library in Simi Valley was the site where Tsai met McCarthy and a bipartisan group of congressional leaders. It was the second high-profile meeting between an American official and Taiwan's president.

China also sanctioned the Hudson Institute, which hosted an event and presented Tsai with its global leadership award on March 30.

The sanctioned groups included Asia-based groups --The Prospect Foundation and the Council of Asian Liberals and Democrats for their involvement in promoting Taiwan's independence.

"[The] Taiwan issue is the core of China's core interests. The Chinese government and Chinese people will never agree to anyone making a fuss about the one-China issue," President Xi told European Commission President Ursula von der Leyen during a meeting in Beijing on Thursday.

It was his first comment after the US House Speaker McCarthy met Tsai, which Beijing sharply criticised.

"Anyone who expects China to compromise on the Taiwan question could only be wishful thinking and self-defeating," Xi was quoted as saying by the state-run Xinhua news agency.

Speaking to reporters after the meeting, von der Leyen said the Taiwan issue had been discussed and she had told Xi that "the threat to use force to change the status quo is unacceptable. It is important that some of the tensions that might occur should be resolved through dialogue", Hong Kong-based South China Morning Post reported.

On Friday's sanctions, the foreign ministry in Beijing said that both American institutions were banned from having exchanges, cooperation, and other activities with any individuals, universities or institutions in China.

"We want to stress China will take resolute measures to safeguard its sovereignty and territorial integrity," Chinese Foreign Ministry spokesperson Mao Ning said at a media briefing.

She also sought to dismiss a question on how Beijing can integrate Taiwan, which follows a multiple-party democratic system with that of China's one-party rule headed by the ruling Communist Party.

The Taiwan question is not about democracy but about China's territorial integrity and reunification and Taiwan is an inalienable part of China's territory, Mao said.

"The sovereignty and territory of China have never been divided and will never be divided," she asserted.

"Some countries support Taiwan in the name of democracy and use the Taiwan question to contain China. This move is dangerous and gets nowhere. Taiwan's future lies in the development of cross-strait relations and reunification with the mainland," she added.

The difference in systems is not a barrier to reunification or an excuse for division, Mao said and advocated the 'one country-two systems' formula which Beijing sought to apply to Hong Kong.

Peaceful reunification and the 'one country two systems' take Taiwan's realities into full account and help to achieve peace and stability after re-unification, she said.

"It is the basic principle to resolving the Taiwan question and the best way for realising reunification," she said.

The sanctions came a day after China vowed reprisals against Taiwan.

China and the US also flexed their naval might by deploying aircraft carriers in a rare showdown in the Taiwan Strait.

Under its longstanding "One China" policy, the US acknowledges China's position that Taiwan is part of China, but has never officially recognised Beijing's claim to the island of 23 million. Under the Taiwan Relations Act, it is also bound by law to provide the democratic island with the means to defend itself.

Meanwhile, Taiwan's foreign ministry on Friday said the head of state of the Republic of China (Taiwan) exercises a basic right of a sovereign nation when travelling to other countries to engage in diplomatic activities. China has no right to intervene.

"China is overreacting when it uses this as a pretext to further suppress Taiwan's international space and impose so-called sanctions on related individuals and organisations. Such irrational behaviour not only increases the Taiwanese people's antipathy to China but also exposes the erratic and absurd nature of the communist regime," Taiwan's foreign ministry said in a statement.