Malaysia's anti-graft commission says it wants a review of the attorney-general's decision to clear prime minister Najib Razak of criminal charges over a multi-million dollar scandal.

The commission's decision scuttled a call by Mr Najib to end the controversy despite his failure to explain why almost $US700 million ($990 million) was transferred into his personal bank accounts in 2013.

Attorney-General Mohamed Apandi Ali's order to shutdown the commission's investigation into the mysterious money transfers has provoked outrage and derision in the country Mr Najib has led for seven years.

Reuters quotes a source at the commission saying investigators had last month recommended that Mr Najib be charged with criminal misappropriation over the transfers.

"It's a pretty straightforward case. We had made recommendations for charges to be filed that the attorney-general has instead chosen to reject," said the source, who declined to be identified or to elaborate on the commission's findings.

The independent news website Malaysiakini also quotes sources saying the commission had proposed three charges against Mr Najib under the penal code relating to "dishonest misappropriation of property".

The website quotes sources saying the charges related the transfer of money originating from a company owned by the Finance Ministry called SRC.

The allegations are potentially explosive because SRC handles the pensions of government employees.

Malaysiakini said it could not obtain official confirmation about the charges, while Mr Najib has repeatedly denied any wrong-doing.

The commission said in a statement it will ask two panels, including the Operations Review Panel set-up to monitor its operations, to review Mr Apandi's decision.

Hours later the commission's strategic communications director Rohaizad Yaakob said the review request was part of its normal case management procedure prior to closing a case, adding that it should not be interpreted as rejecting the decision.

Mr Rohaizad also said that any statement made by any individual is not the official view of the commission.

Opposition MP Lim Kit Siang said he believes the commission issued the second statement due to pressure from Mr Najib's embattled government.

"It clearly shows that the anti-corruption commission made recommendations for action to be taken against Mr Najib but this was rejected, that's why they sought a review," he said.

Mr Apandi announced on Tuesday that money transferred to Mr Najib was a legal "personal donation" from Saudi Arabia's royal family and that $US620 million was returned five months later.

But authorities in Saudi Arabia have failed to confirm any transfers to or from Mr Najib's accounts, deepening the scandal that has prompted growing calls for the prime minister to resign, including from within his long-ruling United Malays National Organisation (UMNO).

Opposition MPs are demanding to know what happened to the $US61 million that, according to Mr Apandi, was not sent back to the Saudi Royal family from Mr Najib's account.

They also want to know who specifically donated the money, why it was donated and why it took more than six months for the government to say where the money came from.

The Wall Street Journal has reported the money flowed to Mr Najib's account through an anonymous British Virgin Islands company and a Swiss private bank account wholly owned by an Abu Dhabi sovereign wealth fund that is intertwined with Malaysia's heavily indebted sovereign fund 1Malaysia Development Berhad, which Mr Najib established in 2009 and still oversees through chairmanship of an advisory committee.

Former prime minister Mahathir Mohamad, Mr Najib's fiercest critic, said in a blog that having so much money in Mr Najib's accounts was wrong in itself, and the attorney-general's role as both judge and prosecutor amounted to an injustice.

Mr Najib, the British-educated son of a former prime minister, has maintained the backing of powerful division chiefs in his party despite the escalating scandal that has engulfed his leadership for months, analysts say.

The divisions have long benefited from largesse that has flowed through the UMNO ranks.

Mr Najib has replaced critics in his government with loyalists, sacked the previous attorney-general who had been investigating him and cracked down on the media.

Following Mr Apandi's announcement, Mr Najib said the controversy has been an "unnecessary distraction" for the country and claimed that "now the matter has been comprehensively put to rest" it was time for Malaysians to unite and move on.

With agencies