UMNO leaders said the withdrawal of support means Muhyiddin no longer commands a majority in parliament.
Muhyiddin met with key advisers late into the night and on Wednesday had an audience with Malaysia's king, Sultan Abdullah Ahmad Shah, whose support is important in Malaysian politics.
"In the meeting, I informed the king that I have sufficient declaration letters which has convinced me that I still have the confidence of the majority of MPs in the parliament at the moment," he said in a televised address.
"Hence the stepping down of myself as prime minister under the constitution... does not arise," he added.
"A vote of confidence for my leadership will be proposed in parliament which will meet in September."
Muhyiddin said the king agreed to his proposal.
Malaysia's premier took power last year at the head of a scandal-hit coalition but his government is in crisis after key allies withdrew support, and he has been heavily criticised for his handling of a worsening coronavirus outbreak.
The country has recorded 17,105 new Covid-19 cases Tuesday, raising the infection total to 1,163,291, with more than 9,500 deaths.
Parliament last month began sitting for the first time this year, but a final session scheduled for Monday was cancelled after the discovery of several coronavirus cases in the legislature.
Muhyiddin's rivals say the cancellation was an excuse to dodge a no-confidence vote.
Political activities had been suspended under a state of emergency, ostensibly to fight the coronavirus outbreak. The emergency officially ended on Sunday, although a nationwide lockdown.