SINGAPORE, Jan 21 (Reuters) - Singapore Telecommunications , Southeast Asia's largest telecoms firm, and ridehailing-to-payments firm Grab Holdings Ltd, have each bought a 16.3% stake in PT Bank Fama International to pursue banking opportunities in Indonesia.

Indonesian conglomerate Elang Mahkota Teknologi Tbk (Emtek), the majority owner of the bank, said on Friday that it sold the stakes to units of Singtel and Grab to "accelerate and expand business growth" of Bank Fama.

In a statement to the Indonesian bourse, Emtek said that once the share issuance is completed, it will end up owning 62.76% in the bank, while another firm will own just under 5%.

Singtel and Grab are each paying 500 billion rupiah ($35 million) for their individual stakes. Emtek owns the stake in Banka Fama through a fully-owned unit.

Grab, Southeast Asia's biggest ridehailing and food delivery firm and operator of a fast-growing financial services business, confirmed it had bought a minority stake in Bank Fama.

Regional consumer tech groups are expanding in Indonesia, Southeast Asia's largest economy - home to more than 1,500 mostly rural banks operating across the vast archipelago of about 270 million people.

Sea's e-commerce arm Shopee bought a bank last year, while payments and ridehailing group Gojek bought a stake in Bank Jago.

Earlier on Friday, Singtel said one of its wholly owned subsidiaries had acquired 2.4 billion new shares in Bank Fama, for $35 million.

Singtel, which has been expanding outside its traditional telco business, has a digital banking joint venture in Singapore with Grab. The joint venture has also applied for a digital banking licence in Malaysia. ($1 = 14,335.0000 rupiah) (Reporting by Anshuman Daga and Aravindan in Singapore; Editing by Ed Davies, Martin Petty)