Beijing warned Taiwan's new president Tsai Ing-wen against seeking independence Friday, cautioning that peace would be "impossible" if she made any moves to formally break away.

The remarks came just hours after Tsai's inauguration speech struck a conciliatory note, calling for a "positive dialogue" with China on fraught cross-strait ties in her much-anticipated address.

China and Taiwan split in 1949 after the Kuomintang nationalist forces lost a civil war to the Communists, although Taiwan has never declared an official breakaway.

But Beijing still sees self-ruling Taiwan as part of its territory awaiting reunification.

While Tsai has pledged to maintain the status quo with Beijing, authorities there are highly suspicious of her and her Democratic Progressive Party, which is traditionally pro-independence.

"If 'independence' is pursued, it will be impossible to have peace and stability in the Taiwan Straits," the Taiwan Affairs Office said in a statement after Tsai was sworn in.

"Independence is the greatest disaster for the peaceful development of peace in the Taiwan straits and the peaceful development of cross-straits relations," it said.

Relations with Beijing have already cooled since Tsai won the presidency, with China putting pressure on her to back its "one China" message -- the bedrock of the thaw under outgoing leader Ma Ying-jeou.

Tsai and the DPP have never recognised the concept and she showed no sign of changing that stance in her speech, clearly irking Beijing.

Tsai took office as the island's first female president after winning a landslide victory in January to defeat the ruling Kuomintang, ending an eight-year rapprochement with Beijing under Ma.

Voters felt Ma had moved too close to China and Tsai swept in with a campaign to restore Taiwanese pride.

But she sought to cast Taiwan as a force for peace in front of a jubilant crowd of more than 20,000 at the presidential palace in Taipei.

"The two governing parties across the strait must set aside the baggage of history, and engage in positive dialogue, for the benefit of the people on both sides," she said.

However, without mentioning China by name, she said Taiwan needed to end its dependency on the mainland for trade, "to bid farewell to our past reliance on a single market".

She also expressed the island's commitment to its democratic freedoms.

- 'Knee-jerk reaction' -

Analysts said Tsai had gone as far as she could to placate Beijing, without making any specific commitments, or alienating her China-wary supporters.

"Tsai tried to strike a conciliatory tone given the lack of trust between the two sides," said Tang Shao-cheng, a political scientist at Taipei's National Chengchi University.

But observers agreed Beijing was never likely to be satisfied without a compromise on the "one China" issue.

China's response was a "knee-jerk reaction, repeating its existing warning against Taiwan independence", said Professor Shih Cheng-feng at Taiwan's Dong Hwa University.

Official mainland Chinese news outlets largely snubbed the inauguration, while searches for Tsai's name and "Taiwan" were blocked on social media.

In celebrations likely to have irritated Beijing, the "Pride of Taiwan" inauguration pageant revolved around Taiwan's unique culture and history.

"Tsai Ing-wen is the first woman president in Taiwan's history so I want to witness this sacred moment," said teacher Chen Su-mei, 48, who joined the celebrations.

A small group of pro-independence activists demonstrated outside the presidential palace.

Rival pro-China activists railed against them, demanding unification with the mainland.

The controversial "one China" concept is enshrined in a tacit agreement between Beijing and the KMT known as the "1992 consensus".

In her speech Friday Tsai reiterated her previous stance of acknowledging the 1992 meeting had happened, but without endorsing the "one China" principle.

Beijing criticised her for taking an "ambiguous approach" to the issue in her speech.

Washington -- Taiwan's main ally and leading arms supplier -- congratulated Tsai and the people of Taiwan on the "peaceful transition" of power.

Tsai is under pressure from the United States not to rock the boat with Beijing and risk destabilising the region.