BEIJING, June 3 (Reuters) - China has alleged that the British Secret Intelligence Service MI6 turned two staff members of unnamed Chinese central state organs into spies for the British government, its State Security Ministry said in a statement on Monday.

The ministry said the case against the two spies, a married couple, is under further investigation.

China and Britain have for months traded accusations over perceived spying that threatens their respective national securities.

In January, China revealed an espionage case in which it said MI6 used a foreigner in China to collect secrets and information.

Britain in April charged two people with providing prejudicial information to China and last month charged three people with assisting Hong Kong's foreign intelligence service in Britain.

In its statement, the Chinese ministry said the spy with the surname Wang studied in the UK in 2015 under an exchange programme and had been invited to dinners and tours surreptitiously arranged by the MI6 during that period.

Wang was said to have "a strong desire for money" and was lured into a part-time consulting opportunity with high remuneration before MI6 personnel approached him to work to serve the British government with promises of even bigger monetary rewards, as well as security. He agreed.

After espionage training, MI6 commanded Wang to return to China to collect important information related to the Chinese government.

The ministry said MI6 also persuaded Wang to turn his wife, who worked at a "core government unit", for double the money. The wife, surnamed Zhou, eventually agreed.