The Southeast Asian nation has been in turmoil since a reformist government headed by Mahathir Mohamad, which included Anwar, collapsed in February amid bitter infighting.
Malaysian opposition leader Anwar Ibrahim says he presented the nation's king with evidence that he has enough support among lawmakers to topple the prime minister and form a new government.
Anwar on Tuesday said the monarch pledged to abide by the constitution, and would consult leaders from other parties before making a decision.
He declined to give details, urging Malaysians to be patient and give the king space to review the evidence.
“These documents made it abundantly clear that we have registered a formidable and convincing majority among parliamentarians,” Anwar told a news conference after the royal meeting.
“Prime Minister Muhyiddin Yassin has lost his majority and therefore, it would be appropriate for him to resign.”
Anwar said he had the support of over 120 lawmakers in the 222-strong parliament, disclosing his numbers for the first time since his announcement last month he had secured a majority from federal lawmakers to form a new government.
Anwar said it was now up to King Al Sultan Abdullah to decide on the next step.
The king plays a largely ceremonial role, but he can appoint a prime minister who in his view is likely to command a majority.
The king could also dissolve parliament and trigger elections on the prime minister's advice.
In March, the king appointed Muhyiddin as the prime minister after the unexpected resignation of Mahathir Mohamad, saying he believed Muhyiddin commanded majority support in parliament.
Alhamdulillah, menjunjung setinggi kasih kepada Kebawah Duli Yang Maha Mulia SPB YDPA Sultan Abdullah, di atas perkenan Baginda menerima saya mengadap hari ini.— Anwar Ibrahim (@anwaribrahim) October 13, 2020
Saya berdoa agar Baginda Tuanku sentiasa dikurniakan keafiaatan dan keberkatan. pic.twitter.com/3pCDSz52u5
The power struggle comes as Malaysia, already grappling with an economy battered by the novel coronavirus, faces a renewed surge in infections.
Should Anwar succeed in securing the post, it would be the culmination of a 22-year long quest, which included nearly 10 years in jail on charges he denied. It would also mean Malaysia would have its third prime minister this year.
But scepticism over Anwar's challenge remains as no major party has offered a clear declaration of support. One party, which is a member of the ruling coalition, has said some of its lawmakers supported Anwar.
"Should the meeting fail to translate into an actionable outcome, his credibility will be affected and this may push the opposition bloc to find another PM candidate," said Shazwan Mustafa Kamal, senior associate at political consultancy Vriens & Partners.
Muhyiddin, whose seven-month-old administration has survived on a razor-thin parliamentary majority, had earlier dismissed Anwar's claims as a "mere allegation" and told him to prove his majority through a constitutional process.
Leaders in Muhyiddin's Perikatan Nasional coalition issued a statement on Monday declaring full support for Muhyiddin.