* Taiwan warns of increasing threat from enemies
* China says warships on routine drill
* Pentagon closely monitoring Chinese military activities (Adds Taiwan comment)
By J.R. Wu
TAIPEI, Dec 27 (Reuters) - Taiwan warned on Tuesday that "the threat of our enemies is growing day by day", as Chinese warships led by the country's sole aircraft carrier sailed towards the island province of Hainan through the South China Sea on a routine drill.
China has given few details of what the Soviet-built Liaoning aircraft carrier is up to, save that it is on a routine exercise. Taiwan has said the aircraft carrier skirted waters outside of its eastern air defence identification zone.
The carrier is expected to arrive at a Chinese military base on the southern Chinese island of Hainan late on Tuesday, Taiwan's defence ministry said.
The drill comes amid renewed tension over Taiwan, which China claims as its own and says is ineligible for state-to-state relations, following U.S. President-elect Donald Trump's telephone call with the island's president that upset Beijing.
"The threat of our enemies is growing day by day. We should always be maintaining our combat alertness," Taiwan Defence Minister Feng Shih-kuan said. "We need to strengthen the training (of our soldiers) so that they can not only survive in battle but also destroy the enemy and accomplish the mission."
Feng's remarks were given in a speech Tuesday at a ministry event marking the promotion of senior military officers.
China's air force conducted long-range drills this month above the East and South China Seas that rattled Japan and Taiwan. China said those exercises were also routine.
China claims most of the South China Sea, through which about $5 trillion in ship-borne trade passes every year. Neighbours Brunei, Malaysia, the Philippines, Taiwan and Vietnam also have claims.
The Pentagon did not directly comment on the latest drill but said that the United States recognises lawful use of sea and airspace in accordance to international law.
"We continue to closely monitor developments in the region. We do not have specific comments on China's recent naval activities, but we continue to observe a range of ongoing Chinese military activity in the region," Pentagon spokesman Gary Ross told Reuters.
The Liaoning has taken part in previous exercises, including in the South China Sea, but China is years away from perfecting carrier operations similar to those the United States has practised for decades.
Last December, the defence ministry confirmed China was building a second aircraft carrier but its launch date is unclear. The aircraft carrier programme is a state secret.
Beijing could build multiple aircraft carriers over the next 15 years, the Pentagon said in a report last year.
China has claimed sovereignty over Taiwan since 1949, when Mao Zedong's Communist forces won the Chinese civil war and Chiang Kai-shek's Nationalists fled to the island. Beijing has vowed to bring Taiwan under its rule, by force if necessary. (Reporting by J.R. Wu; Additional reporting by Tim Kelly in Tokyo; Writing by Ben Blanchard; Editing by Nick Macfie)