Mr Anwar met the nation’s king on Tuesday to show evidence that he has majority support in Parliament to form a new government and unseat prime minister Muhyiddin Yassin, who has only a thin two-seat majority in the house.
Police said in a statement on Thursday they received 113 complaints over the list of 121 politicians allegedly backing Mr Anwar that has been spread on social media.
They did not disclose details of the complaints.
They said they are investigating the complaints under provisions in the penal code covering statements of public mischief and a multimedia law on the improper use of network facilities to harass someone.
Mr Anwar has been summoned to give his statement.
Mr Anwar, 73, evaded reporters by using another entrance at the police headquarters, local media reported.
He has not commented on the police investigation but earlier said the king will meet leaders of political parties to verify his claim.
The political tussle is likely to drag on as King Sultan Abdullah Sultan Ahmad Shah has postponed the meetings with party leaders due to restrictions imposed in Kuala Lumpur this week because of a surge in coronavirus cases.
The monarch on Thursday advised political leaders to “avoid plunging the country into another political crisis” during the pandemic.
In a statement, he urged politicians to settle their dispute through negotiations and under legal processes based on the constitution.
Mr Muhyiddin, who took power in March after causing the collapse of Mr Anwar’s reformist alliance, has previously dismissed Mr Anwar’s claim of having secured the support of a majority of politicians to unseat him.
He said he would leave it to the king to decide but faced increasing pressure this week.
After Mr Anwar’s audience with the king, the key ally in Mr Muhyiddin’s ruling coalition threatened to withdraw support for the government amid anger over being sidelined despite being the biggest party.
Several politicians, both in the ruling coalition and the opposition, have also sought a vote of no confidence against Mr Muhyiddin when Parliament resumes November 2.
But the motion may be thwarted by the house speaker, who is aligned with the prime minister.
Mr Anwar’s Alliance of Hope won elections in 2018 but collapsed after Mr Muhyiddin withdrew his party and joined with the opposition to form a Malay-centric government in March.
Then-prime minister Mahathir Mohamad resigned in protest, saying he would not work with parties accused of corruption that he ousted in the 2018 polls.
If Mr Anwar succeeds, it would mark a dramatic comeback after his roller-coaster political journey since the 1990s.