TAIPEI, June 23 (Reuters) - A major Taiwanese Buddhist group said on Wednesday that it was hoping to buy 5 million doses of BioNTech SE's COVID-19 vaccine, joining Foxconn and TSMC in trying to secure vaccines for the island.

Taiwan's government has millions of vaccines on order but has been hampered by global supply shortages, though Japan and the United States this month donated 3.74 million doses as the island deals with a cluster of domestic infections.

The Tzu Chi Foundation said that after "initial progress" had been made in sourcing the shots, it had submitted application documents to the government to be allowed to buy 5 million BioNTech doses.

BioNTech did not immediately respond to a request for comment.

Taiwan's government said last week it would allow Terry Gou, the billionaire founder of Apple Inc supplier Foxconn, and Taiwan Semiconductor Manufacturing Co Ltd to negotiate on its behalf for COVID-19 vaccines.

Both are proposing buying 5 million BioNTech doses each, to donate to the government.

The government says BioNTech told Gou it would only sell to governments.

Taiwan's own deal with BioNTech fell through this year, with the government blaming it on pressure from Beijing, though it says talks are continuing with the company.

China denied the accusation, saying Taiwan was free to obtain the vaccines through Shanghai Fosun Pharmaceutical Group Co Ltd, which has a contract with BioNTech to sell the vaccines in mainland China, Hong Kong, Macau and Taiwan.

Another Taiwanese group, the Buddha Light International Association, had proposed importing up to 500,000 shots of Johnson & Johnson's vaccine.

But the company said it was only negotiating with government bodies and supranational organisations like the European Commission for vaccine purchases. (Reporting by Ben Blanchard Editing by Robert Birsel)