Mr Najib's opponents claim he used an array of agencies, companies and banks connected with 1MDB to move more than $675 million into his personal bank account. The Malaysian leader denies the 1MDB link and says he has done nothing wrong as the funds were from an unnamed Middle Eastern donor and were not for his personal gain.
Hong Kong police are investigating bank deposits of more than $250 million allegedly made at a Credit Suisse branch in the city. Credit Suisse declined to comment on the claims.
The Hong Kong investigation was prompted by a report to the authorities by Khairuddin Abu Hassan, a vocal critic of 1MDB and a senior member of Mr Najib's ruling United Malays National Organisation until he was sacked this year, ostensibly because he was bankrupt.
Mr Khairuddin alleges the deposits were made through four companies linked to Mr Najib: Alliance Assets International, Cityfield Enterprises, Bartingale International and Wonder Quest Investment.
"These companies are highly questionable," he wrote on his Facebook page. "I have asked the police in Hong Kong to make a detailed and comprehensive investigation of the companies' financial resources and transactions."
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Hong Kong police confirmed they had received the request and that investigations were under way. The companies could not be reached for comment.
Mr Khairuddin said he flew to Hong Kong to report the allegations because he had lost faith in investigations by authorities in Malaysia.
"I wanted police from another country to investigate comprehensively and transparently and without any influence from the prime minister of Malaysia," he wrote. "Honestly and sincerely, I no longer have trust or confidence in the police, the [central bank] and the Office of the Attorney-General."
But the latest allegations prompted a furious response from Mr Najib's side, which accused Mr Khairuddin of lodging "false and politically motivated police reports".
"The prime minister does not control any Credit Suisse bank accounts in Hong Kong, whether in his name or the name of the companies mentioned," a government spokesman said in a statement.
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The statement accused Mr Khairuddin of pushing the same agenda as Mahathir Mohamad, the former premier who was once Mr Najib's patron but is now campaigning to topple him.
Mr Najib has sparked accusations that he is cracking down on the country's institutions to stymie investigations into 1MDB, which has racked up debts of more than $11 billion. The premier replaced the attorney-general on the grounds of ill-health, fired his deputy prime minister for disloyalty and halted the work of a committee investigating the corruption allegations by promoting four officials.
Mr Khairuddin also requested that the police look into possible transactions between 1MDB and companies run by Jho Low, a high-flying Hong Kong-based tycoon. Mr Low, who has previously denied wrongdoing in the 1MDB case, did not respond to a request for comment.