Muhyiddin, who has a razor thin majority in parliament, is under pressure from unhappy coalition partners who have demanded more powerful positions amid a resurgence in coronavirus cases and a pandemic-battered economy.
Calls for him to resign grew after the king on Sunday rejected his request for him to declare emergency rule amid a leadership challenge. Critics have accused the premier of using the pandemic as a pretext to suspend parliament and avoid a test of his majority.
The United Malays National Organisation (UMNO) party, which had earlier this month threatened to withdraw support for Muhyiddin, said it will now back him as the time has come for national reconciliation between political parties to ensure political stability and to focus efforts on managing the pandemic.
UMNO also said it will not work with opposition leader Anwar Ibrahim's party, rejecting a proposal by former Malaysian premier and now-ruling party lawmaker Najib Razak.
Last month, Anwar declared that he had secured majority support from federal lawmakers to form a new government, sparking the political crisis.
In a Monday meeting of the former ruling Barisan Nasional coalition led by UMNO, Najib asked lawmakers in the alliance to endorse Anwar, three sources familiar with the matter said.
Najib's backing of Anwar marks a striking turnaround in their relationship. Anwar was one of the key leaders in a coalition that defeated Najib in a historic election in 2018.
Muhyiddin has maintained a tenuous alliance with UMNO, whose backing was key in his bid to secure the premiership in March after a bout of political wrangling led to the collapse of the administration led by veteran politician Mahathir Mohamad.
Leaders in UMNO, which had led the country for over 60 years until its defeat in a 2018 election, have balked at playing second fiddle to Muhyiddin's party. Some of UMNO's corruption-tainted leaders, including Najib, have been trying to revive their political fortunes.