TAIPEI, May 17 (Reuters) - Taiwan is in talks with the United States for a share of the COVID-19 vaccine doses President Joe Biden plans to send abroad, Taipei's top official in Washington said, as the island deals with a rare spike in domestic cases.

Biden said the United States would send at least 20 million more vaccine doses abroad by the end of June, marking the first time the United States has shared vaccines authorised for domestic use.

Biden announced on Monday that his administration would send doses of the Pfizer-BioNTech, Moderna and Johnson & Johnson vaccines, on top of 60 million AstraZeneca doses he had already planned to give to other countries.

Hsiao Bi-khim, the de facto Taiwanese ambassador to the United States, told Taiwan's official Central News Agency she had already expressed that Taiwan wanted to be included.

"We are in negotiations and striving for it," Hsiao said, in comments reported on Tuesday.

Hsiao said that although vaccine purchases were the remit of Taiwan's health ministry, her office's role was to talk to the United States about speeding up those requests.

The United States, like most countries, has no formal diplomatic relations with Chinese-claimed Taiwan, but is its most important international backer.

Taiwan has reported more than 700 new domestic infections over the past week, leading to new curbs in the capital, Taipei, and shocking a population that had become accustomed to life carrying on almost normally with the pandemic well under control.

Taiwan has only received about 300,000 shots so far for its more than 23 million people, all AstraZeneca vaccine, and those are rapidly running out.

Taiwan has ordered 20 million more doses, mostly from AstraZeneca but also from Moderna, though global shortages have curtailed supplies.

Taiwan has said it also expected to get more than 1 million AstraZeneca shots via the COVAX vaccine sharing programme for lower-income countries.