“We all know that a country has sovereignty. According to the constitution of the Republic of China, the sovereignty of the Republic of China belongs to the people as a whole.”

“Anyone who holds Republic of China nationality is a citizen of the Republic of China; thus, it is clear that the Republic of China and the People’s Republic of China are not subordinate to each other,” he said.

“Every individual must unite and cherish the nation. Any political party must resist annexation and protect sovereignty, and cannot sacrifice national sovereignty for the sake of political power.”

Lai said that more countries were “openly supporting Taiwan’s international participation” and that it was “evident that Taiwan is a country that belongs to the world, and Taiwan is a reliable force for global peace and prosperity”.

Tsai, who completed two four-year terms, was on hand to greet various overseas guests. Hsiao Bi-khim, the new vice-president who was also sworn in, shed a few tears as she walked out to wave to supporters after the ceremony.

In line with tradition, the United States sent a group of former officials to attend, including Brian Deese, US President Joe Biden’s former top economic adviser, and Richard Armitage, deputy secretary of state under former president George W. Bush.

Laura Rosenberger, chairwoman of the American Institute in Taiwan, US’s de facto embassy in Taipei, was also present.

Beijing sees Taiwan as a breakaway region to be reunited with the mainland, by force if necessary. Most countries, including the US, do not recognise the island as an independent state. But Washington opposes any attempt to take the island by force and is committed to supplying weapons to the island.

Cross-strait relations worsened during Tsai’s time in office, which began in 2016.

As Lai’s swearing-in commenced, Beijing’s Ministry of Commerce added three US companies to its “unreliable entities” list for their involvement in arms sales to Taiwan – Boeing Defence, Space & Security, General Atomics Aeronautical Systems, and General Dynamics Land Systems.

The companies will no longer be allowed to engage in import and export activities related to China, or make new investments in the country. The ministry said it would also ban the firms’ high-level executives from entering China, as well as cancel their work, stay and residence permits.

The ministry would also impose fines on the companies, calculated at twice the value of the arms sales contracts signed since the implementation of the “Unreliable Entities List Regulation”, it said.

The companies must pay the fine within 15 days of the publication of the notice. If they failed to comply with this decision, the unreliable entity list management mechanism would take legal action, including imposing additional fines, according to the announcement.

The Taiwanese defence ministry said the military maintained vigilance over the Taiwan Strait during Lai’s inauguration.

In a statement on Monday, the ministry affirmed that the island’s forces “will persist in employing collaborative intelligence surveillance methods to observe the activities of the People’s Liberation Army”.

The ministry also gave an assurance that “any unforeseen circumstances will be handled in compliance with the National Military Emergency Response Regulations”.

The People’s Liberation Army kept military manoeuvres in the Taiwan Strait at a low level on Monday, after ramping up air and sea patrols near the island in the past week.

The Taiwanese defence ministry reported six aircraft and seven vessels operating near the island in the 24 hours from Sunday morning. All six aircraft crossed the median line, a notional midpoint between Taiwan and the mainland.

According to the ministry, the PLA sent at least 45 aircraft and six vessels to the Taiwan Strait on Tuesday, in its most intense activity near the island of the week, as well as for the month of May.

A notice published at 6.30am on Monday by Beijing’s top security agency criticised efforts by Washington and Taipei to undermine the one-China principle, which is based on UN General Assembly Resolution 2758, passed in 1971.

The resolution formally expelled Taiwan – under its official name the Republic of China – and switching recognition to Beijing as “the only legitimate representative of China” at the United Nations.

The Ministry for State Security said on its official WeChat account that in recent years, the US has repeatedly claimed that the resolution “only recognises the People’s Republic of China as the sole legitimate representative of China at the United Nations, without touching on the issue of Taiwan’s representation at the UN”.

The ministry’s statement also noted that Washington had even passed laws to recognise Taiwan’s “international independence”, referring to the Taiwan International Solidarity Act, passed by the US House of Representatives.

In a congratulatory message, US Secretary of State Antony Blinken said the partnership between the American and Taiwanese people was “rooted in democratic values” and “continues to broaden and deepen across trade, economic, cultural, and people-to-people ties”.

“We look forward to working with President Lai and across Taiwan’s political spectrum to advance our shared interests and values, deepen our longstanding unofficial relationship, and maintain peace and stability across the Taiwan Strait,” he said.

Pelosi’s visit triggered an enraged response from Beijing, which launched a days-long large-scale military drill around the island.

In a BBC interview ahead of stepping down, Tsai said that if Taiwan and other democracies “deal with the matter very carefully, there’s still a great possibility for us to maintain peace as we all need”.

Reflecting on Pelosi’s visit, Tsai said “there are a lot of communications and diplomacy, the details of which I cannot tell you, but there [was] a lot of work behind the scenes to make it less of an impact on the cross-strait situation”.