The comments by Najib Razak followed a weekend in which pressure on him mounted over allegations of fraud and embezzlement at a debt-ridden, state-owned investment company that he launched and still oversees.
Influential former premier Mahathir Mohamad has waged a months-long campaign for Najib to step aside over the matter, saying it could eventually result in the long-ruling United Malays National Organisation (UMNO) being ousted in future elections.
But some of Najib's own cabinet ministers over the weekend began echoing the calls for a thorough probe into the scandal-tainted company, 1Malaysia Development Berhad (1MDB).
He said the Supreme Council called for the ruling establishment to be "united in resolving any crisis" but added that council members wanted a probe by the auditor-general into 1MDB, which was ordered by Najib in March, to be "sped up".
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Najib's reputation has been hammered this year by a drip-feed of damaging allegations concerning 1MDB.
These include accusations that at least USD 700 million has gone missing in murky overseas financial transactions that critics say have never been fully explained, either by 1MDB or Najib.
It is now believed to be struggling to pay that off, prompting fears that it could default on loans and collapse, rattling the financial system and UMNO's ruling coalition.
Reports of the allegedly lavish lifestyle enjoyed by Najib's family have also stoked public anger.
Najib has vowed there will be no government bailout of 1MDB.
But it was revealed last week that a fund which helps people in the Muslim-majority country to finance trips to Mecca had bought land from 1MDB at prices far above what 1MDB originally paid.