Speaking in a televised address, Muhyiddin said King Al-Sultan Abdullah agreed that he should remain in power pending the confidence vote, even though some members of his coalition have withdrawn support.
Muhyiddin's hold on power has been precarious ever since he emerged as prime minister in March last year, but the influential monarch had hitherto helped him survive in order to avoid political chaos as Malaysia battled surging Covid-19 infections and an economic downturn from multiple lockdowns.
Pressure on him quit erupted again last week, however, after the king issued a rare rebuke of a government move to revoke emergency laws without his approval, an act the palace said ran counter to the constitution.
The United Malays National Organisation (UMNO) party, the biggest bloc in Muhyiddin's ruling alliance, said Muhyiddin had lost legitimacy after the rebuke and that some of its lawmakers had written to the king withdrawing their support.
In a defiant address on national television, Muhyiddin — flanked by nine lawmakers, including the deputy prime minister and UMNO politician Ismail Sabri Yaakob — said there was no question of him resigning.
"I have informed the king that I have received a number of declarations from lawmakers that convinced me that I still have the confidence of the majority of lawmakers at this time," Muhyiddin said.
"However, I am aware that my position as Prime Minister continues to be questioned. Hence, I have informed the King that I will determine my legitimacy as Prime Minister in Parliament," he said.
The UMNO party is split on its support for Muhyiddin, who has governed with a razor-thin majority and led an unstable ruling coalition since coming to power in March 2020.
The Kuala Lumpur Stock Exchange, which had fallen earlier due to political uncertainty, recouped some losses after Muhyiddin's address.
Muhyiddin said the political turmoil was triggered by "certain parties" whose demands he had refused to meet, including freeing individuals facing corruption charges.
"This includes the push for me to interfere with court matters to free a few individuals who are being prosecuted for criminal offences," Muhyiddin said, though he did not name them.
UMNO did not have an immediate comment.
Several UMNO politicians are facing corruption charges, including former premier Najib Razak and party president Ahmad Zahid Hamidi.
Najib was convicted last year and sentenced to 12 years in jail in a case linked to the multi-billion-dollar 1MDB scandal. He has denied wrongdoing and has appealed the ruling.
Ahmad Zahid is also in the middle of a graft trial.
The two were among those who withdrew support for Muhyiddin this week.
Last year, Muhyiddin was picked by the king to form a government along with UMNO and other parties that had been defeated in a 2018 election. But he has constantly been challenged by some UMNO lawmakers.
Multi-ethnic Malaysia is a constitutional monarchy and the king's role is rotated among the nine sultans - the traditional Malay rulers.