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Taiwan has proposed a zero tariff regime with US

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Taiwan ready for talks at any time, foreign minister says

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Taiwan stock market steadies after Monday's plummet

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AmCham Taiwan calls on US to exempt island from trade actions

(Adds Monday comment from White House economic adviser Kevin Hassett, paragraph 6)

By Wen-Yee Lee and Faith Hung

TAIPEI, April 8 (Reuters) - Taiwan can have negotiations with the United States at any time on the tariffs issue, Foreign Minister Lin Chia-lung said on Tuesday, a day after the island's stock market plummeted on trade fears.

Major semiconductor producer Taiwan, hit with a 32% duty, was singled out by the U.S. administration as among the U.S. trading partners with one of the highest trade surpluses with the country.

Taiwan President Lai Ching-te on Sunday proposed a zero-tariffs regime with the United States, and to invest more in the country and remove trade barriers.

Speaking to reporters on the sidelines of parliament, Lin said that Taiwan was ready to talk about a variety of issues with the United States, including investment in and purchases from the country and non-tariff barriers.

"As long as there is a confirmed time and method for negotiations, they can be discussed at any time with the United States," he added.

On Monday, White House economic adviser Kevin Hassett said Taiwan had reached out to discuss the tariffs.

Premier Cho Jung-tai, also speaking at parliament, said Taiwan was indeed one of those U.S. trading partners seeking talks and the government would choose an appropriate time to present Lai's plans to the United States.

Cho declined to give details of talks with the United States, Taiwan's most important international backer despite the lack of formal diplomatic ties.

"We definitely have a comprehensive plan, we have the right people, and we will be able to go and have positive negotiations," he added.

Taiwan's benchmark stock index, which logged its worst fall ever on Monday, down almost 10%, fell another 4% on Tuesday and hit its lowest level in 14 months.

Shares in TSMC, the world's largest contract chipmaker, dropped 3.8%, though semiconductors are so far exempt from the new U.S .tariffs.

Shares in Foxconn, Apple's biggest iPhone maker, dropped almost 10%, their daily down limit, extending their previous day's drop.

While the selling pressure was unrelenting, Tuesday's losses came as Asian stocks bounced off 1-1/2-year lows and U.S. stock futures pointed higher, with markets catching their breath after recent heavy selling on hopes that Washington might be willing to negotiate some of its aggressive tariffs.

Taiwan has repeatedly said its large trade surplus with the United States is due to soaring demand for tech, given its companies are major suppliers to companies like Apple and Nvidia.

In a statement on Tuesday, the American Chamber of Commerce in Taiwan expressed its strong concern about the tariffs, and called on Washington to exempt Taiwan from trade actions that could "jeopardise the stability and trust underpinning the U.S.-Taiwan relationship". (Reporting by Wen-Yee Lee and Faith Hung; Writing and additional reporting by Ben Blanchard; Editing by Stephen Coates, Kim Coghill and Tomasz Janowski)