BANGKOK — The Malaysian police said on Monday that they were opening an investigation into whether government officials, including central bank personnel, were the source of leaked documents purporting to show the transfer of hundreds of millions of dollars into the bank accounts of Prime Minister Najib Razak and his wife.

Mr. Najib, who was already unpopular for imposing a nationwide sales tax in April to pay for large budget shortfalls, has been embroiled in a scandal over billions of dollars that his critics say are missing from a sovereign wealth fund, 1Malaysia Development Berhad, also known as 1MDB.

The leaked documents were part of an investigation into the fund and were published by The Wall Street Journal and a website, Sarawak Report, this month. They purport to show transfers of around $700 million into what are described as Mr. Najib’s personal bank accounts. Sarawak Report also reported cash deposits of two million ringgit, or around $525,000, into the account of Rosmah Mansor, Mr. Najib’s wife, this year.

Mr. Najib’s office did not respond to a request for comment on Monday, but he said in a statement this month that he had “never taken funds for personal gain.” He has also denied that money is missing from the sovereign wealth fund.