The head of the Malaysian Anti-Corruption Commission, who was appointed by Najib in 2016, has resigned but Mahathir said he could also be investigated.
The country's constitutional king Muhammad V last week agreed to grant Anwar a full pardon after a request from Pakatan Harapan leaders.
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. At 92, he is the world's oldest elected leader.
Anwar is expected to address a rally to be held late Wednesday in the district of Petaling Jaya near Kuala Lumpur.
"My answer is simply that we must all firmly resolve to never let our nation sink to the depths it did again and prime minister Mohamad now has a rare second chance to put things right".
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.
He added: "I will play a role in the background even when I step down".
When Mahathir was prime minister in the 1990s, Anwar was his deputy and clear heir-apparent. He had been in hospital recovering from shoulder surgery.
Anwar's release on Wednesday will cap a tumultuous two decades he has endured. Pakatan Harapan's predecessor, Pakatan Rakyat, dealt heavy blows to Barisan Nasional in the 2008 and 2013 elections. He jailed his former deputy on charges of sodomy and corruption.
Anwar and his supporters have long denied the sodomy allegations, saying they were concocted to destroy his political career.
To this day, Mahathir maintains he sacked Anwar following advice from the police, and that it was the courts who decided Anwar's fate - not him.
Also Monday, the graft agency's former investigations and intelligence chief lodged complaints alleging that Najib had used his position to block corruption investigations into the 1MDB fund and several other cases.
"There are many faults committed by the previous government, but we can not do everything in one day, so you have to be patient".
Arrested in 1974 in student protests against rural poverty, Anwar was sentenced to 20 months in jail. "I urge you all to join the people's movement to demand for change".
Swiss prosecutors said Tuesday they wanted to start talks with investigators in Malaysia as soon as possible to better coordinate various criminal probes into the sprawling case.
A person described in the U.S. lawsuits as "Malaysian Official 1" was said to have received more than US$1 billion in 1MDB funds, some of which was used to buy jewellery for the person's wife.
Malaysia's Prime Minister Mahathir Mohamad is seen on video conference screen during the Wall Street Journal CEO Conference in Tokyo, Japan May 15, 2018.
News broke in 2015 that about $700 million allegedly stolen from 1MDB had made its way into Najib's personal bank accounts.
"The pardon timing is fast, and this speaks to the recognition that his conviction was unjust", said Bridget Welsh, a political science professor at the John Cabot University in Rome. Mahathir has ordered him barred from leaving the country.