Mahathir also said he will find a replacement for the head of the anti-corruption authority, after the resignation of former one.
Mahathir had previously said he would remain prime minister for two years before stepping down for Anwar to take over.
Once seen as a potential future leader, he had been jailed on charges of sodomy and corruption after falling out with the government.
Mr Anwar always denied the charges and claimed he was a victim of a political conspiracy.
Mahathir has said he expects to run the government for up to two years but has signalled the reins would be turned over to the Anwar eventually.
Anwar, 70, was convicted of sodomy in 2015 in a case he said was aimed at crushing his alliance, which was making gains against Malaysia's long-ruling coalition government.
Killed in Explosion at Office Building in California
Authorities had not found an explosive device Tuesday night but were searching through debris that was left after the blast. ". This photo taken from video provided by KABC-TV shows a building after an explosion in Aliso Viejo, California, May 15, 2018.
Anwar emerged from the Cheras Rehabilitation Hospital on Wednesday after Malaysia's Pardon Board, which included the current King, made a decision to overturn the 2015 conviction, which is widely accepted to be politically motivated.
Anwar was supposed to speak to the press outside the centre upon his release, but the sheer hubbub from supporters and media seems to have delayed this. The cases against him have been politically motivated. "It is also the recognition that the people have spoken and the royalty are responding to these issues".
Anwar's wife Wan Azizah Wan Ismail, who is the new deputy premier, has said there was no rush for Anwar to take over.
The volatile relationship between the duo has dominated the country's political landscape for over three decades.
Mahathir said his government hasn't asked for help from Interpol to find Low Taek Jho, named as a central figure who allegedly orchestrated the ransacking of 1MDB, but added they "roughly know" where Low is. He was initially supposed to name 10 ministers but appeared to have been stalled by horse-trading over positions.
Anwar will travel directly to the palace after his release.
Texas joins lawsuits against company accused of worsening opioid epidemic
Opioids are a family of drugs that include prescription painkillers such as OxyContin as well as illegal drugs like heroin. Of the top 25 cities for opioid abuse, four are in Texas - Texarkana, Amarillo, Odessa and Longview.
Mahathir said it would be hard to achieve consensus and any decisions will be based on the voice of the majority.
Despite his firebrand reputation, he later confounded liberal supporters in 1982 by joining the conservative United Malays National Organization (UMNO) led by Mahathir.
Mahathir's four-party coalition won a historic election victory over former leader Najib Razak on May 9. Mahathir said he can't suspend Apandi until he is investigated.
But in 1998, they disagreed on how to tackle the Asian financial crisis and fell out. That black eye has become the logo of his People's Justice Party.
Tensions within the ruling coalition, which are likely given differences between Mr Mahathir and Mr Anwar in the past, would raise doubts about the ability of the administration to deliver. He led an opposition alliance to major gains in the last two elections, winning the popular vote in 2013. Without the pardon, Anwar would have been banned from politics for five years due to having a criminal record.
He maintains his innocence, and says on both occasions Mahathir and Najib turned to trumping up charges against him to keep him out of politics.
Golfer's Wife Arrested After Altercation With His Mother
Deputies noted lacerations on the arms of both Lucas and his mother, Hershey Glover, who also had blood on her clothes. Police reportedly saw abrasions and other injuries on Hershey Glover when they arrived to arrest Krista Glover.
His opposition alliance broke up after its Islamist ally left.