(Adds trade by State Street of London in paragraph 3)

By Yena Park, Cynthia Kim and Jihoon Lee

SEOUL, Jan 2 (Reuters) - State Street Bank & Trust Company of Hong Kong made the first dollar/won trade after South Korean authorities opened the interbank market to foreign financial institutions under a pilot programme on Tuesday, sources familiar with the deal said.

The trade was conducted with Hana Bank, according to the sources who declined to be identified as they are not authorised to speak to media.

State Street of London also made a trade in the market, according to one of the sources.

South Korea in October began accepting applications from foreign financial institutions to review permits to participate in the onshore dollar-won interbank market in a bid to encourage more foreign participation.

"This transaction is the first dollar-won transaction concluded in the Seoul foreign exchange market between a registered foreign institution (RFI) located overseas," a Hana Bank official said.

"We are pleased to be the first RFI to participate in the onshore interbank foreign exchange market in Korea. We are excited to expand our capabilities to access the Korean FX market offshore," said Henry Quek, Head of Global Markets, Asia Pacific, State Street.

"It is encouraging that Korea is implementing measures to enhance the market accessibility of its FX market structure. We look forward to supporting our clients to participate in the Korean FX market both onshore and offshore," Quek said.

The government also plans to extend onshore trading hours until 2 a.m. KST (1700 GMT), or the closing of London business hours.

Up until the end of 2023, the Korean won could only be directly traded with the dollar through local banks, for just six-and-a-half hours a day between 9 a.m. (0000 GMT) and 3:30 p.m.

(Reporting by Yena Park, Cynthia Kim and Jihoon Lee; Editing by Jacqueline Wong and Sam Holmes)