Asian leaders have expressed hopes that United States President Donald Trump will deepen alliances and further common interests in a flurry of congratulatory messages, but these belie a sense of unease over the pugnacious "America first" approach as spelt out in his inauguration speech.

And, in a series of rallies across the region, people spoke out against the hate speech, xenophobia and misogyny that had characterised Mr Trump's election campaign.

Over 10,000 people took part in rallies in cities such as Sydney, Melbourne, Wellington, Tokyo and Manila. "We hope people will raise their voices to demand fair treatment regardless of gender, the colour of their skin or sexual orientation," housewife Katherine Hall, 49, told The Sunday Times in Tokyo, where 400 people gathered.

JAPAN

Prime Minister Shinzo Abe, who was the first world leader to meet Mr Trump when the latter was President-elect, said he hopes to arrange an official meeting at the "earliest possible occasion (to) send a message to the world on the importance of the Japan-US alliance".

This alliance, he said, is the "linchpin" of Japan's foreign and security policies. "I'd like to further strengthen the unwavering ties between Japan and the US, based on the relationship of trust between us."

A meeting could take place early next month, local media reported.

The Mainichi daily quoted Mr Masahiko Komura, vice-president of the ruling Liberal Democratic Party, as saying: "If each country begins focusing only on itself, the economic state of the world - including the US - will be disastrous."

TAIWAN

President Tsai Ing-wen tweeted yesterday that she looks forward to "advancing the friendship and partnership" with the US, which her office said was its "most important international ally".

Former premier Yu Shyi-kun, who attended the inauguration ceremony, said in Washington that Taiwan-US ties are at a "historic high".

SOUTH KOREA

Acting President Hwang Kyo Ahn, in his message to Mr Trump, stressed close cooperation to jointly curb the nuclear development of a belligerent Pyongyang.

But media reports have questioned if Mr Trump will be able to deftly resolve the issue, with Yonhap news agency saying Mr Trump has "put the rest of the world on edge".

The Korea Herald added that the country's "withering economy will be put to the test" with Mr Trump's likely protectionist trade policies.

INDIA

Prime Minister Narendra Modi tweeted his hopes to further deepen ties and "realise the full potential of India-US cooperation" with Mr Trump.

But media reports note that India, which has been actively wooing US investment, might suffer from Mr Trump's inward stance. There are also worries that Mr Trump's anti- immigration stance will lead to curbs on the H-1B non-immigrant visa programme used to send Indian workers to the US.

MALAYSIA

Prime Minister Najib Razak said on Facebook that he was confident bilateral ties will strengthen.

"(Mr Trump) takes office after an extraordinary journey which showed that politicians can never take voters for granted. He spoke for an America that felt it had been ignored for too long. Now is the time to govern for all Americans."

PHILIPPINES

Manila respects Mr Trump's "America First" policy, which mirrors President Rodrigo Duterte's own approach to his people, spokesman Ernesto Abella said.

"Our diplomatic ties need to reflect our longstanding relationship, but under terms and conditions that protect our people's interests," he added.

•Reporting by Jermyn Chow in Taipei, Chang May Choon in Seoul, Nirmala Ganapathy in New Delhi, Trinna Leong in Kuala Lumpur and Raul Dancel in Manila.