By Ben Blanchard

TAIPEI (Reuters) -Taiwan is "of course" a country and China lacks both the historical evidence and legal proof to back up its sovereignty claims, President Lai Ching-te said on Sunday in a strong rebuke to Beijing and its stepped up political and military pressure.

China says democratically-governed Taiwan is "sacred" Chinese territory that has belonged to the country since ancient times, and that the island is one of its provinces with no right to be called a state.

Lai and his government strongly reject that view, and have offered talks with China multiple times but have been rejected. China calls Lai a "separatist".

Giving the first of 10 speeches in a series called "uniting the country", Lai drew on Taiwan's history, including the millennia-long connection of its indigenous people to other Austronesians, like native Hawaiians, to show what he said was Taiwan's separate and distinct development from China.

Taiwan's people have a record of opposing invasion, like uprisings against Japan's 1895-1945 colonial rule, and under the last imperial Chinese dynasty, the Qing, Taiwan was only considered a Chinese province for eight years, he added.

"Of course Taiwan is a country," he said at a speech to a Taiwan branch of Rotary International, pointing also to its presidential elections. "But China says no, that Taiwan is not a sovereign country."

China's Taiwan's Affairs Office did not respond to a request for comment outside of office hours. China says the 1971 United Nations resolution, which took away Taipei's seat in the body and gave it to Beijing, is one of the legal bases of its claims.

Lai, who in March called China a "hostile foreign force", said it was "totally wrong" for Beijing to say that U.N. resolution had anything to do with Taiwan's sovereignty as it was only about which government was represented at the body.

China's threat to Taiwan is real, added Lai, pointing to its daily military activities around the island.

"Taiwan's future can only be decided by its 23 million people - does everyone approve of this?" he said, to a round of applause.

The defeated Republic of China government fled to Taiwan in 1949 after losing a civil war with Mao Zedong's communists, and that remains the island's formal name.

(Reporting by Ben Blanchard; Additional reporting by Ryan Woo in Beijing; Editing by Andrew Cawthorne)